Luacháil
\frac{x}{x^{2}-x+1}
Fairsingigh
\frac{x}{x^{2}-x+1}
Graf
Tráth na gCeist
Polynomial
5 fadhbanna cosúil le:
\frac{ x-2 }{ { x }^{ 2 } -x+1 } - \frac{ 1 }{ x+1 } + \frac{ { x }^{ 2 } +x+3 }{ { x }^{ 3 } +1 }
Roinn
Cóipeáladh go dtí an ghearrthaisce
\frac{\left(x-2\right)\left(x+1\right)}{\left(x+1\right)\left(x^{2}-x+1\right)}-\frac{x^{2}-x+1}{\left(x+1\right)\left(x^{2}-x+1\right)}+\frac{x^{2}+x+3}{x^{3}+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^{2}-x+1 agus x+1 ná \left(x+1\right)\left(x^{2}-x+1\right). Méadaigh \frac{x-2}{x^{2}-x+1} faoi \frac{x+1}{x+1}. Méadaigh \frac{1}{x+1} faoi \frac{x^{2}-x+1}{x^{2}-x+1}.
\frac{\left(x-2\right)\left(x+1\right)-\left(x^{2}-x+1\right)}{\left(x+1\right)\left(x^{2}-x+1\right)}+\frac{x^{2}+x+3}{x^{3}+1}
Tá an t-ainmneoir céanna ag \frac{\left(x-2\right)\left(x+1\right)}{\left(x+1\right)\left(x^{2}-x+1\right)} agus \frac{x^{2}-x+1}{\left(x+1\right)\left(x^{2}-x+1\right)} agus, mar sin, is féidir iad a dhealú trína n-uimhreoirí a dhealú.
\frac{x^{2}+x-2x-2-x^{2}+x-1}{\left(x+1\right)\left(x^{2}-x+1\right)}+\frac{x^{2}+x+3}{x^{3}+1}
Déan iolrúcháin in \left(x-2\right)\left(x+1\right)-\left(x^{2}-x+1\right).
\frac{-3}{\left(x+1\right)\left(x^{2}-x+1\right)}+\frac{x^{2}+x+3}{x^{3}+1}
Cumaisc téarmaí comhchosúla in: x^{2}+x-2x-2-x^{2}+x-1.
\frac{-3}{\left(x+1\right)\left(x^{2}-x+1\right)}+\frac{x^{2}+x+3}{\left(x+1\right)\left(x^{2}-x+1\right)}
Fachtóirigh x^{3}+1.
\frac{-3+x^{2}+x+3}{\left(x+1\right)\left(x^{2}-x+1\right)}
Tá an t-ainmneoir céanna ag \frac{-3}{\left(x+1\right)\left(x^{2}-x+1\right)} agus \frac{x^{2}+x+3}{\left(x+1\right)\left(x^{2}-x+1\right)} agus, mar sin, is féidir iad a shuimiú trína n-uimhreoirí a shuimiú.
\frac{x^{2}+x}{\left(x+1\right)\left(x^{2}-x+1\right)}
Cumaisc téarmaí comhchosúla in: -3+x^{2}+x+3.
\frac{x\left(x+1\right)}{\left(x+1\right)\left(x^{2}-x+1\right)}
Fachtóirigh na sloinn nach bhfuil fachtóirithe cheana in \frac{x^{2}+x}{\left(x+1\right)\left(x^{2}-x+1\right)}.
\frac{x}{x^{2}-x+1}
Cealaigh x+1 mar uimhreoir agus ainmneoir.
\frac{\left(x-2\right)\left(x+1\right)}{\left(x+1\right)\left(x^{2}-x+1\right)}-\frac{x^{2}-x+1}{\left(x+1\right)\left(x^{2}-x+1\right)}+\frac{x^{2}+x+3}{x^{3}+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^{2}-x+1 agus x+1 ná \left(x+1\right)\left(x^{2}-x+1\right). Méadaigh \frac{x-2}{x^{2}-x+1} faoi \frac{x+1}{x+1}. Méadaigh \frac{1}{x+1} faoi \frac{x^{2}-x+1}{x^{2}-x+1}.
\frac{\left(x-2\right)\left(x+1\right)-\left(x^{2}-x+1\right)}{\left(x+1\right)\left(x^{2}-x+1\right)}+\frac{x^{2}+x+3}{x^{3}+1}
Tá an t-ainmneoir céanna ag \frac{\left(x-2\right)\left(x+1\right)}{\left(x+1\right)\left(x^{2}-x+1\right)} agus \frac{x^{2}-x+1}{\left(x+1\right)\left(x^{2}-x+1\right)} agus, mar sin, is féidir iad a dhealú trína n-uimhreoirí a dhealú.
\frac{x^{2}+x-2x-2-x^{2}+x-1}{\left(x+1\right)\left(x^{2}-x+1\right)}+\frac{x^{2}+x+3}{x^{3}+1}
Déan iolrúcháin in \left(x-2\right)\left(x+1\right)-\left(x^{2}-x+1\right).
\frac{-3}{\left(x+1\right)\left(x^{2}-x+1\right)}+\frac{x^{2}+x+3}{x^{3}+1}
Cumaisc téarmaí comhchosúla in: x^{2}+x-2x-2-x^{2}+x-1.
\frac{-3}{\left(x+1\right)\left(x^{2}-x+1\right)}+\frac{x^{2}+x+3}{\left(x+1\right)\left(x^{2}-x+1\right)}
Fachtóirigh x^{3}+1.
\frac{-3+x^{2}+x+3}{\left(x+1\right)\left(x^{2}-x+1\right)}
Tá an t-ainmneoir céanna ag \frac{-3}{\left(x+1\right)\left(x^{2}-x+1\right)} agus \frac{x^{2}+x+3}{\left(x+1\right)\left(x^{2}-x+1\right)} agus, mar sin, is féidir iad a shuimiú trína n-uimhreoirí a shuimiú.
\frac{x^{2}+x}{\left(x+1\right)\left(x^{2}-x+1\right)}
Cumaisc téarmaí comhchosúla in: -3+x^{2}+x+3.
\frac{x\left(x+1\right)}{\left(x+1\right)\left(x^{2}-x+1\right)}
Fachtóirigh na sloinn nach bhfuil fachtóirithe cheana in \frac{x^{2}+x}{\left(x+1\right)\left(x^{2}-x+1\right)}.
\frac{x}{x^{2}-x+1}
Cealaigh x+1 mar uimhreoir agus ainmneoir.
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}