Luacháil
\frac{2\left(4x-5\right)}{\left(x-3\right)\left(x+4\right)\left(x^{2}-1\right)}
Difreálaigh w.r.t. x
\frac{2\left(43-130x+67x^{2}+12x^{3}-12x^{4}\right)}{\left(\left(x-3\right)\left(x+4\right)\left(x^{2}-1\right)\right)^{2}}
Graf
Roinn
Cóipeáladh go dtí an ghearrthaisce
\frac{1}{\left(x-1\right)\left(x+1\right)}-\frac{2}{\left(x-1\right)\left(x+4\right)}+\frac{1}{x^{2}-2x-3}
Fachtóirigh x^{2}-1. Fachtóirigh x^{2}+3x-4.
\frac{x+4}{\left(x-1\right)\left(x+1\right)\left(x+4\right)}-\frac{2\left(x+1\right)}{\left(x-1\right)\left(x+1\right)\left(x+4\right)}+\frac{1}{x^{2}-2x-3}
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)\left(x+1\right) agus \left(x-1\right)\left(x+4\right) ná \left(x-1\right)\left(x+1\right)\left(x+4\right). Méadaigh \frac{1}{\left(x-1\right)\left(x+1\right)} faoi \frac{x+4}{x+4}. Méadaigh \frac{2}{\left(x-1\right)\left(x+4\right)} faoi \frac{x+1}{x+1}.
\frac{x+4-2\left(x+1\right)}{\left(x-1\right)\left(x+1\right)\left(x+4\right)}+\frac{1}{x^{2}-2x-3}
Tá an t-ainmneoir céanna ag \frac{x+4}{\left(x-1\right)\left(x+1\right)\left(x+4\right)} agus \frac{2\left(x+1\right)}{\left(x-1\right)\left(x+1\right)\left(x+4\right)} agus, mar sin, is féidir iad a dhealú trína n-uimhreoirí a dhealú.
\frac{x+4-2x-2}{\left(x-1\right)\left(x+1\right)\left(x+4\right)}+\frac{1}{x^{2}-2x-3}
Déan iolrúcháin in x+4-2\left(x+1\right).
\frac{-x+2}{\left(x-1\right)\left(x+1\right)\left(x+4\right)}+\frac{1}{x^{2}-2x-3}
Cumaisc téarmaí comhchosúla in: x+4-2x-2.
\frac{-x+2}{\left(x-1\right)\left(x+1\right)\left(x+4\right)}+\frac{1}{\left(x-3\right)\left(x+1\right)}
Fachtóirigh x^{2}-2x-3.
\frac{\left(-x+2\right)\left(x-3\right)}{\left(x-3\right)\left(x-1\right)\left(x+1\right)\left(x+4\right)}+\frac{\left(x-1\right)\left(x+4\right)}{\left(x-3\right)\left(x-1\right)\left(x+1\right)\left(x+4\right)}
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)\left(x+1\right)\left(x+4\right) agus \left(x-3\right)\left(x+1\right) ná \left(x-3\right)\left(x-1\right)\left(x+1\right)\left(x+4\right). Méadaigh \frac{-x+2}{\left(x-1\right)\left(x+1\right)\left(x+4\right)} faoi \frac{x-3}{x-3}. Méadaigh \frac{1}{\left(x-3\right)\left(x+1\right)} faoi \frac{\left(x-1\right)\left(x+4\right)}{\left(x-1\right)\left(x+4\right)}.
\frac{\left(-x+2\right)\left(x-3\right)+\left(x-1\right)\left(x+4\right)}{\left(x-3\right)\left(x-1\right)\left(x+1\right)\left(x+4\right)}
Tá an t-ainmneoir céanna ag \frac{\left(-x+2\right)\left(x-3\right)}{\left(x-3\right)\left(x-1\right)\left(x+1\right)\left(x+4\right)} agus \frac{\left(x-1\right)\left(x+4\right)}{\left(x-3\right)\left(x-1\right)\left(x+1\right)\left(x+4\right)} agus, mar sin, is féidir iad a shuimiú trína n-uimhreoirí a shuimiú.
\frac{-x^{2}+3x+2x-6+x^{2}+4x-x-4}{\left(x-3\right)\left(x-1\right)\left(x+1\right)\left(x+4\right)}
Déan iolrúcháin in \left(-x+2\right)\left(x-3\right)+\left(x-1\right)\left(x+4\right).
\frac{8x-10}{\left(x-3\right)\left(x-1\right)\left(x+1\right)\left(x+4\right)}
Cumaisc téarmaí comhchosúla in: -x^{2}+3x+2x-6+x^{2}+4x-x-4.
\frac{8x-10}{x^{4}+x^{3}-13x^{2}-x+12}
Fairsingigh \left(x-3\right)\left(x-1\right)\left(x+1\right)\left(x+4\right)
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}