Racionalitzar 1 |
Racionalitzar és eliminar les arrels del denominador. Si hi ha una sola arrel quadrada, es multiplica numerador i denominador per aquesta arrel: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mfrac»«mn»3«/mn»«msqrt»«mn»15«/mn»«/msqrt»«/mfrac»«mo»=«/mo»«mfrac»«mrow»«mn»3«/mn»«mo»§#183;«/mo»«msqrt mathcolor=¨#0000FF¨»«mn mathvariant=¨bold¨»15«/mn»«/msqrt»«/mrow»«mrow»«msqrt»«mn»15«/mn»«/msqrt»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«msqrt mathcolor=¨#0000FF¨»«mn mathvariant=¨bold¨»15«/mn»«/msqrt»«/mrow»«/mfrac»«mo»=«/mo»«mfrac»«mrow»«mn»3«/mn»«mo»§#183;«/mo»«msqrt»«mn»15«/mn»«/msqrt»«/mrow»«mn»15«/mn»«/mfrac»«mo»=«/mo»«mfrac»«msqrt»«mn»15«/mn»«/msqrt»«mn»5«/mn»«/mfrac»«/mrow»«/mstyle»«/math» i es SIMPLIFICA |
Racionalitzar 2 |
Racionalitzar és eliminar les arrels del denominador. Si hi ha una arrel d'índex i superior a 2, es multiplica el numerador i el denominador per una arrel d'índex i i de radicand tal que permeti simplificar el denominador: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mn»12«/mn»«mroot»«mn»4«/mn»«mn»3«/mn»«/mroot»«/mfrac»«mo»=«/mo»«mfrac»«mn»12«/mn»«mroot»«msup»«mn»2«/mn»«mn»2«/mn»«/msup»«mn»3«/mn»«/mroot»«/mfrac»«mo»=«/mo»«mfrac»«mrow»«mn»12«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mroot mathcolor=¨#0000FF¨»«mn mathvariant=¨bold¨»2«/mn»«mn mathvariant=¨bold¨»3«/mn»«/mroot»«/mrow»«mrow»«mroot»«msup»«mn»2«/mn»«mn»2«/mn»«/msup»«mn»3«/mn»«/mroot»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mroot mathcolor=¨#0000FF¨»«mn mathvariant=¨bold¨»2«/mn»«mn mathvariant=¨bold¨»3«/mn»«/mroot»«/mrow»«/mfrac»«mo»=«/mo»«mfrac»«mrow»«mn»12«/mn»«mo»§#183;«/mo»«mroot»«mn»2«/mn»«mn»3«/mn»«/mroot»«/mrow»«mroot»«msup»«mn»2«/mn»«mn»3«/mn»«/msup»«mn»3«/mn»«/mroot»«/mfrac»«mo»=«/mo»«mfrac»«mrow»«mn»12«/mn»«mo»§#183;«/mo»«mroot»«mn»2«/mn»«mn»3«/mn»«/mroot»«/mrow»«mn»2«/mn»«/mfrac»«mo»=«/mo»«mn»6«/mn»«mo»§#183;«/mo»«mroot»«mn»2«/mn»«mn»3«/mn»«/mroot»«/math» i es simplifica |
Format: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mfrac»«mrow»«mn»8«/mn»«mroot»«mn»2«/mn»«mn»5«/mn»«/mroot»«/mrow»«mn»2«/mn»«/mfrac»«/mstyle»«/math»
Com que «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mo mathvariant=¨bold¨ mathcolor=¨#000066¨»#«/mo»«mi mathvariant=¨bold-italic¨ mathcolor=¨#000066¨»e«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#000066¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#000066¨»+«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#000066¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#000066¨»#«/mo»«mi mathvariant=¨bold-italic¨ mathcolor=¨#000066¨»k«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#000066¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#000066¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#000066¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#000066¨»#«/mo»«mi mathvariant=¨bold-italic¨ mathcolor=¨#000066¨»i«/mi»«/mstyle»«/math» cal multiplicar el numerador i el denominador per «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mroot mathcolor=¨#0000FF¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«msup»«mi mathvariant=¨bold¨»c«/mi»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»k«/mi»«/mrow»«/msup»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»i«/mi»«/mrow»«/mroot»«/mstyle»«/math»:
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mfrac mathcolor=¨#0000FF¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a«/mi»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»§#183;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#FF0000¨»§#160;«/mo»«mroot mathcolor=¨#FF0000¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«msup»«mi mathvariant=¨bold¨»c«/mi»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»k«/mi»«/mrow»«/msup»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»i«/mi»«/mrow»«/mroot»«/mrow»«mrow»«mroot»«mrow»«mo mathvariant=¨bold¨»#«/mo»«msup»«mi mathvariant=¨bold¨»c«/mi»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»e«/mi»«/mrow»«/msup»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»i«/mi»«/mrow»«/mroot»«mo»§#183;«/mo»«mo»§#160;«/mo»«mroot mathcolor=¨#FF0000¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«msup»«mi mathvariant=¨bold¨»c«/mi»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»k«/mi»«/mrow»«/msup»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»i«/mi»«/mrow»«/mroot»«/mrow»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#000066¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mfrac mathcolor=¨#0000FF¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a«/mi»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»§#183;«/mo»«mo mathvariant=¨bold¨»§#160;«/mo»«mroot»«mrow»«mo mathvariant=¨bold¨»#«/mo»«msup»«mi mathvariant=¨bold¨»c«/mi»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»k«/mi»«/mrow»«/msup»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»i«/mi»«/mrow»«/mroot»«/mrow»«mroot»«mrow»«mo mathvariant=¨bold¨»#«/mo»«msup»«mi mathvariant=¨bold¨»c«/mi»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»e«/mi»«mo mathvariant=¨bold¨»+«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»k«/mi»«/mrow»«/msup»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»i«/mi»«/mrow»«/mroot»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mfrac mathcolor=¨#0000FF¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a«/mi»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»§#183;«/mo»«mo mathvariant=¨bold¨»§#160;«/mo»«mroot»«mrow»«mo mathvariant=¨bold¨»#«/mo»«msup»«mi mathvariant=¨bold¨»c«/mi»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»k«/mi»«/mrow»«/msup»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»i«/mi»«/mrow»«/mroot»«/mrow»«mroot»«mrow»«mo mathvariant=¨bold¨»#«/mo»«msup»«mi mathvariant=¨bold¨»c«/mi»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»i«/mi»«/mrow»«/msup»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»i«/mi»«/mrow»«/mroot»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mfrac mathcolor=¨#0000FF¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a«/mi»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»§#183;«/mo»«mo mathvariant=¨bold¨»§#160;«/mo»«mroot»«mrow»«mo mathvariant=¨bold¨»#«/mo»«msup»«mi mathvariant=¨bold¨»c«/mi»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»k«/mi»«/mrow»«/msup»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»i«/mi»«/mrow»«/mroot»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»c«/mi»«/mrow»«/mfrac»«/mstyle»«/math»
Només falta simplifica si s'escau.
]]>Format: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mfrac»«mrow»«mn»8«/mn»«mroot»«mn»2«/mn»«mn»5«/mn»«/mroot»«/mrow»«mn»2«/mn»«/mfrac»«/mstyle»«/math»
Com que «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mo mathvariant=¨bold¨ mathcolor=¨#000066¨»#«/mo»«mi mathvariant=¨bold-italic¨ mathcolor=¨#000066¨»e«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#000066¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#000066¨»+«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#000066¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#000066¨»#«/mo»«mi mathvariant=¨bold-italic¨ mathcolor=¨#000066¨»k«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#000066¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#000066¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#000066¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#000066¨»#«/mo»«mi mathvariant=¨bold-italic¨ mathcolor=¨#000066¨»i«/mi»«/mstyle»«/math» cal multiplicar el numerador i el denominador per «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mroot mathcolor=¨#0000FF¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«msup»«mi mathvariant=¨bold¨»c«/mi»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»k«/mi»«/mrow»«/msup»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»i«/mi»«/mrow»«/mroot»«/mstyle»«/math»:
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mfrac mathcolor=¨#0000FF¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a«/mi»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»§#183;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#FF0000¨»§#160;«/mo»«mroot mathcolor=¨#FF0000¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«msup»«mi mathvariant=¨bold¨»c«/mi»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»k«/mi»«/mrow»«/msup»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»i«/mi»«/mrow»«/mroot»«/mrow»«mrow»«mroot»«mrow»«mo mathvariant=¨bold¨»#«/mo»«msup»«mi mathvariant=¨bold¨»c«/mi»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»e«/mi»«/mrow»«/msup»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»i«/mi»«/mrow»«/mroot»«mo»§#183;«/mo»«mo»§#160;«/mo»«mroot mathcolor=¨#FF0000¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«msup»«mi mathvariant=¨bold¨»c«/mi»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»k«/mi»«/mrow»«/msup»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»i«/mi»«/mrow»«/mroot»«/mrow»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#000066¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mfrac mathcolor=¨#0000FF¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a«/mi»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»§#183;«/mo»«mo mathvariant=¨bold¨»§#160;«/mo»«mroot»«mrow»«mo mathvariant=¨bold¨»#«/mo»«msup»«mi mathvariant=¨bold¨»c«/mi»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»k«/mi»«/mrow»«/msup»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»i«/mi»«/mrow»«/mroot»«/mrow»«mroot»«mrow»«mo mathvariant=¨bold¨»#«/mo»«msup»«mi mathvariant=¨bold¨»c«/mi»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»e«/mi»«mo mathvariant=¨bold¨»+«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»k«/mi»«/mrow»«/msup»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»i«/mi»«/mrow»«/mroot»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mfrac mathcolor=¨#0000FF¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a«/mi»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»§#183;«/mo»«mo mathvariant=¨bold¨»§#160;«/mo»«mroot»«mrow»«mo mathvariant=¨bold¨»#«/mo»«msup»«mi mathvariant=¨bold¨»c«/mi»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»k«/mi»«/mrow»«/msup»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»i«/mi»«/mrow»«/mroot»«/mrow»«mroot»«mrow»«mo mathvariant=¨bold¨»#«/mo»«msup»«mi mathvariant=¨bold¨»c«/mi»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»i«/mi»«/mrow»«/msup»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»i«/mi»«/mrow»«/mroot»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mfrac mathcolor=¨#0000FF¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a«/mi»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»§#183;«/mo»«mo mathvariant=¨bold¨»§#160;«/mo»«mroot»«mrow»«mo mathvariant=¨bold¨»#«/mo»«msup»«mi mathvariant=¨bold¨»c«/mi»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»k«/mi»«/mrow»«/msup»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»i«/mi»«/mrow»«/mroot»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»c«/mi»«/mrow»«/mfrac»«/mstyle»«/math»
Només falta simplifica si s'escau.
]]>Format: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mfrac»«mrow»«mn»8«/mn»«mroot»«mn»2«/mn»«mn»5«/mn»«/mroot»«/mrow»«mn»2«/mn»«/mfrac»«/mstyle»«/math»
Com que «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mo mathvariant=¨bold¨ mathcolor=¨#000066¨»#«/mo»«mi mathvariant=¨bold-italic¨ mathcolor=¨#000066¨»e«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#000066¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#000066¨»+«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#000066¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#000066¨»#«/mo»«mi mathvariant=¨bold-italic¨ mathcolor=¨#000066¨»k«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#000066¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#000066¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#000066¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#000066¨»#«/mo»«mi mathvariant=¨bold-italic¨ mathcolor=¨#000066¨»i«/mi»«/mstyle»«/math» cal multiplicar el numerador i el denominador per «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mroot mathcolor=¨#0000FF¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«msup»«mi mathvariant=¨bold¨»c«/mi»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»k«/mi»«/mrow»«/msup»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»i«/mi»«/mrow»«/mroot»«/mstyle»«/math»:
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mfrac mathcolor=¨#0000FF¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a«/mi»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»§#183;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#FF0000¨»§#160;«/mo»«mroot mathcolor=¨#FF0000¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«msup»«mi mathvariant=¨bold¨»c«/mi»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»k«/mi»«/mrow»«/msup»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»i«/mi»«/mrow»«/mroot»«/mrow»«mrow»«mroot»«mrow»«mo mathvariant=¨bold¨»#«/mo»«msup»«mi mathvariant=¨bold¨»c«/mi»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»e«/mi»«/mrow»«/msup»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»i«/mi»«/mrow»«/mroot»«mo»§#183;«/mo»«mo»§#160;«/mo»«mroot mathcolor=¨#FF0000¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«msup»«mi mathvariant=¨bold¨»c«/mi»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»k«/mi»«/mrow»«/msup»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»i«/mi»«/mrow»«/mroot»«/mrow»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#000066¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mfrac mathcolor=¨#0000FF¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a«/mi»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»§#183;«/mo»«mo mathvariant=¨bold¨»§#160;«/mo»«mroot»«mrow»«mo mathvariant=¨bold¨»#«/mo»«msup»«mi mathvariant=¨bold¨»c«/mi»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»k«/mi»«/mrow»«/msup»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»i«/mi»«/mrow»«/mroot»«/mrow»«mroot»«mrow»«mo mathvariant=¨bold¨»#«/mo»«msup»«mi mathvariant=¨bold¨»c«/mi»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»e«/mi»«mo mathvariant=¨bold¨»+«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»k«/mi»«/mrow»«/msup»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»i«/mi»«/mrow»«/mroot»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mfrac mathcolor=¨#0000FF¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a«/mi»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»§#183;«/mo»«mo mathvariant=¨bold¨»§#160;«/mo»«mroot»«mrow»«mo mathvariant=¨bold¨»#«/mo»«msup»«mi mathvariant=¨bold¨»c«/mi»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»k«/mi»«/mrow»«/msup»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»i«/mi»«/mrow»«/mroot»«/mrow»«mroot»«mrow»«mo mathvariant=¨bold¨»#«/mo»«msup»«mi mathvariant=¨bold¨»c«/mi»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»i«/mi»«/mrow»«/msup»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»i«/mi»«/mrow»«/mroot»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mfrac mathcolor=¨#0000FF¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a«/mi»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»§#183;«/mo»«mo mathvariant=¨bold¨»§#160;«/mo»«mroot»«mrow»«mo mathvariant=¨bold¨»#«/mo»«msup»«mi mathvariant=¨bold¨»c«/mi»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»k«/mi»«/mrow»«/msup»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»i«/mi»«/mrow»«/mroot»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»c«/mi»«/mrow»«/mfrac»«/mstyle»«/math»
Només falta simplifica si s'escau.
]]>Racionalitzar 3 |
Racionalitzar és eliminar les arrels del denominador. Si hi ha una suma o una diferència d'arrels al denominador, es multiplica el numerador i el denominador pel conjugat per aplicar (a+b)(a-b)=a2-b2 Si no hi ha arrels al numerador: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mn»26«/mn»«mrow»«msqrt»«mn»7«/mn»«/msqrt»«mo»-«/mo»«msqrt»«mn»3«/mn»«/msqrt»«/mrow»«/mfrac»«mo»=«/mo»«mfrac»«mrow»«mn»26«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mfenced mathcolor=¨#0000FF¨»«mrow»«msqrt»«mn mathvariant=¨bold¨»7«/mn»«/msqrt»«mo mathvariant=¨bold¨»+«/mo»«msqrt»«mn mathvariant=¨bold¨»3«/mn»«/msqrt»«/mrow»«/mfenced»«/mrow»«mrow»«mfenced»«mrow»«msqrt»«mn»7«/mn»«/msqrt»«mo»-«/mo»«msqrt»«mn»3«/mn»«/msqrt»«/mrow»«/mfenced»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mfenced mathcolor=¨#0000FF¨»«mrow»«msqrt»«mn mathvariant=¨bold¨»7«/mn»«/msqrt»«mo mathvariant=¨bold¨»+«/mo»«msqrt»«mn mathvariant=¨bold¨»3«/mn»«/msqrt»«/mrow»«/mfenced»«/mrow»«/mfrac»«mo»=«/mo»«mfrac»«mrow»«mn»26«/mn»«mo»§#183;«/mo»«mfenced»«mrow»«msqrt»«mn»7«/mn»«/msqrt»«mo»+«/mo»«msqrt»«mn»3«/mn»«/msqrt»«/mrow»«/mfenced»«/mrow»«mrow»«mn mathcolor=¨#7F0000¨»7«/mn»«mo mathcolor=¨#7F0000¨»-«/mo»«mn mathcolor=¨#7F0000¨»3«/mn»«/mrow»«/mfrac»«mspace linebreak=¨newline¨/»«mo»=«/mo»«mfrac»«mrow»«mn»26«/mn»«mo»§#183;«/mo»«mfenced»«mrow»«msqrt»«mn»7«/mn»«/msqrt»«mo»+«/mo»«msqrt»«mn»3«/mn»«/msqrt»«/mrow»«/mfenced»«/mrow»«mn»4«/mn»«/mfrac»«mo»=«/mo»«mfrac»«mrow»«mn»13«/mn»«mo»§#183;«/mo»«mfenced»«mrow»«msqrt»«mn»7«/mn»«/msqrt»«mo»+«/mo»«msqrt»«mn»3«/mn»«/msqrt»«/mrow»«/mfenced»«/mrow»«mn»2«/mn»«/mfrac»«/math» i es simplifica |
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mfrac mathcolor=¨#000066¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a«/mi»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»m«/mi»«mo mathvariant=¨bold¨»-«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»n«/mi»«/mrow»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#000066¨»§#183;«/mo»«mfrac mathcolor=¨#000066¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»m«/mi»«mo mathvariant=¨bold¨»+«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»n«/mi»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»m«/mi»«mo mathvariant=¨bold¨»+«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»n«/mi»«/mrow»«/mfrac»«/mrow»«/mstyle»«/math» perquè «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mfenced mathcolor=¨#0000FF¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»m«/mi»«mo mathvariant=¨bold¨»-«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»n«/mi»«/mrow»«/mfenced»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mfenced mathcolor=¨#0000FF¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»m«/mi»«mo mathvariant=¨bold¨»+«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»n«/mi»«/mrow»«/mfenced»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«msup mathcolor=¨#0000FF¨»«mfenced mathcolor=¨#0000FF¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»m«/mi»«/mrow»«/mfenced»«mn mathvariant=¨bold¨»2«/mn»«/msup»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»-«/mo»«msup mathcolor=¨#0000FF¨»«mfenced mathcolor=¨#0000FF¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»n«/mi»«/mrow»«/mfenced»«mn mathvariant=¨bold¨»2«/mn»«/msup»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«/mrow»«/mstyle»«/math»
i s'eliminen les arrels.
]]>Com que «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mfenced mathcolor=¨#000066¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»m«/mi»«mo mathvariant=¨bold¨»-«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»n«/mi»«/mrow»«/mfenced»«mfenced mathcolor=¨#000066¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»m«/mi»«mo mathvariant=¨bold¨»+«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»n«/mi»«/mrow»«/mfenced»«mo mathvariant=¨bold¨ mathcolor=¨#000066¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#000066¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#000066¨»c«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#000066¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#000066¨»-«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#000066¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#000066¨»d«/mi»«/mrow»«/mstyle»«/math», ens queda
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mfrac mathcolor=¨#000066¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a«/mi»«mfenced»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»m«/mi»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»+«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»n«/mi»«/mrow»«/mfenced»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»c«/mi»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»-«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»d«/mi»«/mrow»«/mfrac»«/mstyle»«/math» per simplificar, si es pot.
]]>«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mfrac mathcolor=¨#000066¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a«/mi»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»m«/mi»«mo mathvariant=¨bold¨»-«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»n«/mi»«/mrow»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#000066¨»§#183;«/mo»«mfrac mathcolor=¨#000066¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»m«/mi»«mo mathvariant=¨bold¨»+«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»n«/mi»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»m«/mi»«mo mathvariant=¨bold¨»+«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»n«/mi»«/mrow»«/mfrac»«/mrow»«/mstyle»«/math» perquè «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mfenced mathcolor=¨#0000FF¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»m«/mi»«mo mathvariant=¨bold¨»-«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»n«/mi»«/mrow»«/mfenced»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mfenced mathcolor=¨#0000FF¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»m«/mi»«mo mathvariant=¨bold¨»+«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»n«/mi»«/mrow»«/mfenced»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«msup mathcolor=¨#0000FF¨»«mfenced mathcolor=¨#0000FF¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»m«/mi»«/mrow»«/mfenced»«mn mathvariant=¨bold¨»2«/mn»«/msup»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»-«/mo»«msup mathcolor=¨#0000FF¨»«mfenced mathcolor=¨#0000FF¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»n«/mi»«/mrow»«/mfenced»«mn mathvariant=¨bold¨»2«/mn»«/msup»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«/mrow»«/mstyle»«/math»
i s'eliminen les arrels.
]]>Com que «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mfenced mathcolor=¨#000066¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»m«/mi»«mo mathvariant=¨bold¨»-«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»n«/mi»«/mrow»«/mfenced»«mfenced mathcolor=¨#000066¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»m«/mi»«mo mathvariant=¨bold¨»+«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»n«/mi»«/mrow»«/mfenced»«mo mathvariant=¨bold¨ mathcolor=¨#000066¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#000066¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#000066¨»c«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#000066¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#000066¨»-«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#000066¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#000066¨»d«/mi»«/mrow»«/mstyle»«/math», ens queda
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mfrac mathcolor=¨#000066¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a«/mi»«mfenced»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»m«/mi»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»+«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»n«/mi»«/mrow»«/mfenced»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»c«/mi»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»-«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»d«/mi»«/mrow»«/mfrac»«/mstyle»«/math» per simplificar, si es pot.
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Com que «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mfenced mathcolor=¨#000066¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»m«/mi»«mo mathvariant=¨bold¨»+«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»n«/mi»«/mrow»«/mfenced»«mfenced mathcolor=¨#000066¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»m«/mi»«mo mathvariant=¨bold¨»-«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»n«/mi»«/mrow»«/mfenced»«mo mathvariant=¨bold¨ mathcolor=¨#000066¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#000066¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#000066¨»c«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#000066¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#000066¨»-«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#000066¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#000066¨»d«/mi»«/mstyle»«/math», et queda
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mfrac mathcolor=¨#000066¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a«/mi»«mfenced»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»m«/mi»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»-«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»n«/mi»«/mrow»«/mfenced»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»c«/mi»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»-«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»d«/mi»«/mrow»«/mfrac»«/mstyle»«/math» per simplificar, si es pot.
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Com que «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mfenced mathcolor=¨#000066¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»m«/mi»«mo mathvariant=¨bold¨»+«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»n«/mi»«/mrow»«/mfenced»«mfenced mathcolor=¨#000066¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»m«/mi»«mo mathvariant=¨bold¨»-«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»n«/mi»«/mrow»«/mfenced»«mo mathvariant=¨bold¨ mathcolor=¨#000066¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#000066¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#000066¨»c«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#000066¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#000066¨»-«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#000066¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#000066¨»d«/mi»«/mstyle»«/math», et queda
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mfrac mathcolor=¨#000066¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a«/mi»«mfenced»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»m«/mi»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»-«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»n«/mi»«/mrow»«/mfenced»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»c«/mi»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»-«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»d«/mi»«/mrow»«/mfrac»«/mstyle»«/math» per simplificar, si es pot.
]]>Racionalitzar 4 |
Racionalitzar és eliminar les arrels del denominador. Si hi ha una suma o una diferència d'arrels al denominador, es multiplica el numerador i el denominador pel conjugat per aplicar (a+b)(a-b)=a2-b2 Si hi ha arrels al numerador: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«mn»2«/mn»«mo»+«/mo»«msqrt»«mn»5«/mn»«/msqrt»«/mrow»«mrow»«msqrt»«mn»5«/mn»«/msqrt»«mo»+«/mo»«msqrt»«mn»3«/mn»«/msqrt»«/mrow»«/mfrac»«mo»=«/mo»«mfrac»«mrow»«mfenced mathcolor=¨#191919¨»«mrow»«mn»2«/mn»«mo»+«/mo»«msqrt»«mn»5«/mn»«/msqrt»«/mrow»«/mfenced»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mfenced mathcolor=¨#0000FF¨»«mrow»«msqrt»«mn mathvariant=¨bold¨»5«/mn»«/msqrt»«mo mathvariant=¨bold¨»-«/mo»«msqrt»«mn mathvariant=¨bold¨»3«/mn»«/msqrt»«/mrow»«/mfenced»«/mrow»«mrow»«mfenced»«mrow»«msqrt»«mn»5«/mn»«/msqrt»«mo»+«/mo»«msqrt»«mn»3«/mn»«/msqrt»«/mrow»«/mfenced»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mfenced mathcolor=¨#0000FF¨»«mrow»«msqrt»«mn mathvariant=¨bold¨»5«/mn»«/msqrt»«mo mathvariant=¨bold¨»-«/mo»«msqrt»«mn mathvariant=¨bold¨»3«/mn»«/msqrt»«/mrow»«/mfenced»«/mrow»«/mfrac»«mo»=«/mo»«mfrac»«mrow»«mn»5«/mn»«mo»-«/mo»«mn»2«/mn»«msqrt»«mn»3«/mn»«/msqrt»«mo»+«/mo»«mn»2«/mn»«msqrt»«mn»5«/mn»«/msqrt»«mo»-«/mo»«msqrt»«mn»15«/mn»«/msqrt»«/mrow»«mrow»«mn mathcolor=¨#7F0000¨»5«/mn»«mo mathcolor=¨#7F0000¨»-«/mo»«mn mathcolor=¨#7F0000¨»3«/mn»«/mrow»«/mfrac»«mspace linebreak=¨newline¨/»«mo»=«/mo»«mfrac»«mrow»«mn»5«/mn»«mo»-«/mo»«mn»2«/mn»«msqrt»«mn»3«/mn»«/msqrt»«mo»+«/mo»«mn»2«/mn»«msqrt»«mn»5«/mn»«/msqrt»«mo»-«/mo»«msqrt»«mn»15«/mn»«/msqrt»«/mrow»«mn»2«/mn»«/mfrac»«/math» i es simplifica |
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Com que «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mfenced mathcolor=¨#000066¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»m«/mi»«mo mathvariant=¨bold¨»-«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»n«/mi»«/mrow»«/mfenced»«mfenced mathcolor=¨#000066¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»m«/mi»«mo mathvariant=¨bold¨»+«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»n«/mi»«/mrow»«/mfenced»«mo mathvariant=¨bold¨ mathcolor=¨#000066¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#000066¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#000066¨»c«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#000066¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#000066¨»-«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#000066¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#000066¨»d«/mi»«/mrow»«/mstyle»«/math», ens queda
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mfrac mathcolor=¨#000066¨»«mrow»«mo mathvariant=¨bold¨»(«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a«/mi»«mo mathvariant=¨bold¨»)«/mo»«mfenced»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»m«/mi»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»+«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»n«/mi»«/mrow»«/mfenced»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»c«/mi»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»-«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»d«/mi»«/mrow»«/mfrac»«/mstyle»«/math» per simplificar, si es pot.
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Com que «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mfenced mathcolor=¨#000066¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»m«/mi»«mo mathvariant=¨bold¨»+«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»n«/mi»«/mrow»«/mfenced»«mfenced mathcolor=¨#000066¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»m«/mi»«mo mathvariant=¨bold¨»-«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»n«/mi»«/mrow»«/mfenced»«mo mathvariant=¨bold¨ mathcolor=¨#000066¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#000066¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#000066¨»c«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#000066¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#000066¨»-«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#000066¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#000066¨»d«/mi»«/mstyle»«/math», ens queda
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mfrac mathcolor=¨#000066¨»«mrow»«mo mathvariant=¨bold¨»(«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a«/mi»«mo mathvariant=¨bold¨»)«/mo»«mfenced»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»m«/mi»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»-«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»n«/mi»«/mrow»«/mfenced»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»c«/mi»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»-«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»d«/mi»«/mrow»«/mfrac»«/mstyle»«/math» per simplificar, si es pot.
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