Evalwa
-\frac{2\left(y^{2}+1\right)}{3\left(y^{2}-1\right)}
Espandi
-\frac{2\left(y^{2}+1\right)}{3\left(y^{2}-1\right)}
Sehem
Ikkupjat fuq il-klibbord
\left(\frac{x\left(y-1\right)}{\left(y-1\right)\left(y+1\right)}-\frac{x\left(y+1\right)}{\left(y-1\right)\left(y+1\right)}\right)\times \frac{x+xy^{2}}{3x^{2}}
Biex iżżid jew tnaqqas l-espressjonijiet, espandihom biex id-denominaturi tagħhom ikunu l-istess. L-inqas multiplu komuni ta' y+1 u y-1 huwa \left(y-1\right)\left(y+1\right). Immultiplika \frac{x}{y+1} b'\frac{y-1}{y-1}. Immultiplika \frac{x}{y-1} b'\frac{y+1}{y+1}.
\frac{x\left(y-1\right)-x\left(y+1\right)}{\left(y-1\right)\left(y+1\right)}\times \frac{x+xy^{2}}{3x^{2}}
Billi \frac{x\left(y-1\right)}{\left(y-1\right)\left(y+1\right)} u \frac{x\left(y+1\right)}{\left(y-1\right)\left(y+1\right)} għandhom l-istess denominatur, naqqashom billi tnaqqas in-numeraturi tagħhom.
\frac{xy-x-xy-x}{\left(y-1\right)\left(y+1\right)}\times \frac{x+xy^{2}}{3x^{2}}
Agħmel il-multiplikazzjonijiet fi x\left(y-1\right)-x\left(y+1\right).
\frac{-2x}{\left(y-1\right)\left(y+1\right)}\times \frac{x+xy^{2}}{3x^{2}}
Ikkombina termini simili f'xy-x-xy-x.
\frac{-2x}{\left(y-1\right)\left(y+1\right)}\times \frac{x\left(y^{2}+1\right)}{3x^{2}}
Iffattura l-espressjonijiet li mhumiex diġà fatturati f'\frac{x+xy^{2}}{3x^{2}}.
\frac{-2x}{\left(y-1\right)\left(y+1\right)}\times \frac{y^{2}+1}{3x}
Annulla x fin-numeratur u d-denominatur.
\frac{-2x\left(y^{2}+1\right)}{\left(y-1\right)\left(y+1\right)\times 3x}
Immultiplika \frac{-2x}{\left(y-1\right)\left(y+1\right)} b'\frac{y^{2}+1}{3x} billi timmultiplika n-numeratur bin-numeratur u d-denominatur bid-denominatur.
\frac{-2\left(y^{2}+1\right)}{3\left(y-1\right)\left(y+1\right)}
Annulla x fin-numeratur u d-denominatur.
\frac{-2y^{2}-2}{3\left(y-1\right)\left(y+1\right)}
Uża l-propjetà distributtiva biex timmultiplika -2 b'y^{2}+1.
\frac{-2y^{2}-2}{\left(3y-3\right)\left(y+1\right)}
Uża l-propjetà distributtiva biex timmultiplika 3 b'y-1.
\frac{-2y^{2}-2}{3y^{2}-3}
Uża l-propjetà distributtiva biex timmultiplika 3y-3 b'y+1 u kkombina termini simili.
\left(\frac{x\left(y-1\right)}{\left(y-1\right)\left(y+1\right)}-\frac{x\left(y+1\right)}{\left(y-1\right)\left(y+1\right)}\right)\times \frac{x+xy^{2}}{3x^{2}}
Biex iżżid jew tnaqqas l-espressjonijiet, espandihom biex id-denominaturi tagħhom ikunu l-istess. L-inqas multiplu komuni ta' y+1 u y-1 huwa \left(y-1\right)\left(y+1\right). Immultiplika \frac{x}{y+1} b'\frac{y-1}{y-1}. Immultiplika \frac{x}{y-1} b'\frac{y+1}{y+1}.
\frac{x\left(y-1\right)-x\left(y+1\right)}{\left(y-1\right)\left(y+1\right)}\times \frac{x+xy^{2}}{3x^{2}}
Billi \frac{x\left(y-1\right)}{\left(y-1\right)\left(y+1\right)} u \frac{x\left(y+1\right)}{\left(y-1\right)\left(y+1\right)} għandhom l-istess denominatur, naqqashom billi tnaqqas in-numeraturi tagħhom.
\frac{xy-x-xy-x}{\left(y-1\right)\left(y+1\right)}\times \frac{x+xy^{2}}{3x^{2}}
Agħmel il-multiplikazzjonijiet fi x\left(y-1\right)-x\left(y+1\right).
\frac{-2x}{\left(y-1\right)\left(y+1\right)}\times \frac{x+xy^{2}}{3x^{2}}
Ikkombina termini simili f'xy-x-xy-x.
\frac{-2x}{\left(y-1\right)\left(y+1\right)}\times \frac{x\left(y^{2}+1\right)}{3x^{2}}
Iffattura l-espressjonijiet li mhumiex diġà fatturati f'\frac{x+xy^{2}}{3x^{2}}.
\frac{-2x}{\left(y-1\right)\left(y+1\right)}\times \frac{y^{2}+1}{3x}
Annulla x fin-numeratur u d-denominatur.
\frac{-2x\left(y^{2}+1\right)}{\left(y-1\right)\left(y+1\right)\times 3x}
Immultiplika \frac{-2x}{\left(y-1\right)\left(y+1\right)} b'\frac{y^{2}+1}{3x} billi timmultiplika n-numeratur bin-numeratur u d-denominatur bid-denominatur.
\frac{-2\left(y^{2}+1\right)}{3\left(y-1\right)\left(y+1\right)}
Annulla x fin-numeratur u d-denominatur.
\frac{-2y^{2}-2}{3\left(y-1\right)\left(y+1\right)}
Uża l-propjetà distributtiva biex timmultiplika -2 b'y^{2}+1.
\frac{-2y^{2}-2}{\left(3y-3\right)\left(y+1\right)}
Uża l-propjetà distributtiva biex timmultiplika 3 b'y-1.
\frac{-2y^{2}-2}{3y^{2}-3}
Uża l-propjetà distributtiva biex timmultiplika 3y-3 b'y+1 u kkombina termini simili.
Eżempji
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Ekwazzjoni simultanja
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\frac { d } { d x } \frac { ( 3 x ^ { 2 } - 2 ) } { ( x - 5 ) }
Integrazzjoni
\int _ { 0 } ^ { 1 } x e ^ { - x ^ { 2 } } d x
Limiti
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