Luacháil
\frac{5+3x-5x^{2}}{x^{2}\left(1-x^{2}\right)}
Difreálaigh w.r.t. x
\frac{-10x^{4}+9x^{3}+20x^{2}-3x-10}{x^{3}\left(x^{2}-1\right)^{2}}
Graf
Tráth na gCeist
Polynomial
\frac { 2 } { x ^ { 2 } - x } + \frac { 5 } { x ^ { 2 } - x ^ { 3 } } + \frac { 3 } { x ^ { 2 } - 1 }
Roinn
Cóipeáladh go dtí an ghearrthaisce
\frac{2}{x\left(x-1\right)}+\frac{5}{\left(-x+1\right)x^{2}}+\frac{3}{x^{2}-1}
Fachtóirigh x^{2}-x. Fachtóirigh x^{2}-x^{3}.
\frac{2x}{\left(x-1\right)x^{2}}+\frac{5\left(-1\right)}{\left(x-1\right)x^{2}}+\frac{3}{x^{2}-1}
Chun cothromóidí a shuimiú nó a dhealú, fairsingigh iad chun a n-ainmneoirí a mheaitseáil. Is é an t-iolrach is lú coitianta de x\left(x-1\right) agus \left(-x+1\right)x^{2} ná \left(x-1\right)x^{2}. Méadaigh \frac{2}{x\left(x-1\right)} faoi \frac{x}{x}. Méadaigh \frac{5}{\left(-x+1\right)x^{2}} faoi \frac{-1}{-1}.
\frac{2x+5\left(-1\right)}{\left(x-1\right)x^{2}}+\frac{3}{x^{2}-1}
Tá an t-ainmneoir céanna ag \frac{2x}{\left(x-1\right)x^{2}} agus \frac{5\left(-1\right)}{\left(x-1\right)x^{2}} agus, mar sin, is féidir iad a shuimiú trína n-uimhreoirí a shuimiú.
\frac{2x-5}{\left(x-1\right)x^{2}}+\frac{3}{x^{2}-1}
Déan iolrúcháin in 2x+5\left(-1\right).
\frac{2x-5}{\left(x-1\right)x^{2}}+\frac{3}{\left(x-1\right)\left(x+1\right)}
Fachtóirigh x^{2}-1.
\frac{\left(2x-5\right)\left(x+1\right)}{\left(x-1\right)\left(x+1\right)x^{2}}+\frac{3x^{2}}{\left(x-1\right)\left(x+1\right)x^{2}}
Chun cothromóidí a shuimiú nó a dhealú, fairsingigh iad chun a n-ainmneoirí a mheaitseáil. Is é an t-iolrach is lú coitianta de \left(x-1\right)x^{2} agus \left(x-1\right)\left(x+1\right) ná \left(x-1\right)\left(x+1\right)x^{2}. Méadaigh \frac{2x-5}{\left(x-1\right)x^{2}} faoi \frac{x+1}{x+1}. Méadaigh \frac{3}{\left(x-1\right)\left(x+1\right)} faoi \frac{x^{2}}{x^{2}}.
\frac{\left(2x-5\right)\left(x+1\right)+3x^{2}}{\left(x-1\right)\left(x+1\right)x^{2}}
Tá an t-ainmneoir céanna ag \frac{\left(2x-5\right)\left(x+1\right)}{\left(x-1\right)\left(x+1\right)x^{2}} agus \frac{3x^{2}}{\left(x-1\right)\left(x+1\right)x^{2}} agus, mar sin, is féidir iad a shuimiú trína n-uimhreoirí a shuimiú.
\frac{2x^{2}+2x-5x-5+3x^{2}}{\left(x-1\right)\left(x+1\right)x^{2}}
Déan iolrúcháin in \left(2x-5\right)\left(x+1\right)+3x^{2}.
\frac{5x^{2}-3x-5}{\left(x-1\right)\left(x+1\right)x^{2}}
Cumaisc téarmaí comhchosúla in: 2x^{2}+2x-5x-5+3x^{2}.
\frac{5x^{2}-3x-5}{x^{4}-x^{2}}
Fairsingigh \left(x-1\right)\left(x+1\right)x^{2}
Samplaí
Cothromóid chearnach
{ x } ^ { 2 } - 4 x - 5 = 0
Triantánacht
4 \sin \theta \cos \theta = 2 \sin \theta
Cothromóid líneach
y = 3x + 4
Uimhríocht
699 * 533
Maitrís
\left[ \begin{array} { l l } { 2 } & { 3 } \\ { 5 } & { 4 } \end{array} \right] \left[ \begin{array} { l l l } { 2 } & { 0 } & { 3 } \\ { -1 } & { 1 } & { 5 } \end{array} \right]
Cothromóid chomhuaineach
\left. \begin{cases} { 8x+2y = 46 } \\ { 7x+3y = 47 } \end{cases} \right.
Difreáil
\frac { d } { d x } \frac { ( 3 x ^ { 2 } - 2 ) } { ( x - 5 ) }
Comhtháthú
\int _ { 0 } ^ { 1 } x e ^ { - x ^ { 2 } } d x
Teorainneacha
\lim _{x \rightarrow-3} \frac{x^{2}-9}{x^{2}+2 x-3}