Luacháil
\frac{x^{2}+bx+3x+17}{\left(x+1\right)\left(x+3\right)}
Fairsingigh
\frac{x^{2}+bx+3x+17}{\left(x+1\right)\left(x+3\right)}
Graf
Tráth na gCeist
Algebra
\frac { x } { x + 3 } \div \frac { x ^ { 2 } + x } { x ^ { 2 } + b x + 8 } + \frac { 3 x - 3 } { x ^ { 2 } - 1 }
Roinn
Cóipeáladh go dtí an ghearrthaisce
\frac{x\left(x^{2}+bx+8\right)}{\left(x+3\right)\left(x^{2}+x\right)}+\frac{3x-3}{x^{2}-1}
Roinn \frac{x}{x+3} faoi \frac{x^{2}+x}{x^{2}+bx+8} trí \frac{x}{x+3} a mhéadú faoi dheilín \frac{x^{2}+x}{x^{2}+bx+8}.
\frac{x\left(x^{2}+bx+8\right)}{x\left(x+1\right)\left(x+3\right)}+\frac{3x-3}{x^{2}-1}
Fachtóirigh na sloinn nach bhfuil fachtóirithe cheana in \frac{x\left(x^{2}+bx+8\right)}{\left(x+3\right)\left(x^{2}+x\right)}.
\frac{x^{2}+bx+8}{\left(x+1\right)\left(x+3\right)}+\frac{3x-3}{x^{2}-1}
Cealaigh x mar uimhreoir agus ainmneoir.
\frac{x^{2}+bx+8}{\left(x+1\right)\left(x+3\right)}+\frac{3\left(x-1\right)}{\left(x-1\right)\left(x+1\right)}
Fachtóirigh na sloinn nach bhfuil fachtóirithe cheana in \frac{3x-3}{x^{2}-1}.
\frac{x^{2}+bx+8}{\left(x+1\right)\left(x+3\right)}+\frac{3}{x+1}
Cealaigh x-1 mar uimhreoir agus ainmneoir.
\frac{x^{2}+bx+8}{\left(x+1\right)\left(x+3\right)}+\frac{3\left(x+3\right)}{\left(x+1\right)\left(x+3\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+3\right) agus x+1 ná \left(x+1\right)\left(x+3\right). Méadaigh \frac{3}{x+1} faoi \frac{x+3}{x+3}.
\frac{x^{2}+bx+8+3\left(x+3\right)}{\left(x+1\right)\left(x+3\right)}
Tá an t-ainmneoir céanna ag \frac{x^{2}+bx+8}{\left(x+1\right)\left(x+3\right)} agus \frac{3\left(x+3\right)}{\left(x+1\right)\left(x+3\right)} agus, mar sin, is féidir iad a shuimiú trína n-uimhreoirí a shuimiú.
\frac{x^{2}+bx+8+3x+9}{\left(x+1\right)\left(x+3\right)}
Déan iolrúcháin in x^{2}+bx+8+3\left(x+3\right).
\frac{x^{2}+bx+17+3x}{\left(x+1\right)\left(x+3\right)}
Cumaisc téarmaí comhchosúla in: x^{2}+bx+8+3x+9.
\frac{x^{2}+bx+17+3x}{x^{2}+4x+3}
Fairsingigh \left(x+1\right)\left(x+3\right)
\frac{x\left(x^{2}+bx+8\right)}{\left(x+3\right)\left(x^{2}+x\right)}+\frac{3x-3}{x^{2}-1}
Roinn \frac{x}{x+3} faoi \frac{x^{2}+x}{x^{2}+bx+8} trí \frac{x}{x+3} a mhéadú faoi dheilín \frac{x^{2}+x}{x^{2}+bx+8}.
\frac{x\left(x^{2}+bx+8\right)}{x\left(x+1\right)\left(x+3\right)}+\frac{3x-3}{x^{2}-1}
Fachtóirigh na sloinn nach bhfuil fachtóirithe cheana in \frac{x\left(x^{2}+bx+8\right)}{\left(x+3\right)\left(x^{2}+x\right)}.
\frac{x^{2}+bx+8}{\left(x+1\right)\left(x+3\right)}+\frac{3x-3}{x^{2}-1}
Cealaigh x mar uimhreoir agus ainmneoir.
\frac{x^{2}+bx+8}{\left(x+1\right)\left(x+3\right)}+\frac{3\left(x-1\right)}{\left(x-1\right)\left(x+1\right)}
Fachtóirigh na sloinn nach bhfuil fachtóirithe cheana in \frac{3x-3}{x^{2}-1}.
\frac{x^{2}+bx+8}{\left(x+1\right)\left(x+3\right)}+\frac{3}{x+1}
Cealaigh x-1 mar uimhreoir agus ainmneoir.
\frac{x^{2}+bx+8}{\left(x+1\right)\left(x+3\right)}+\frac{3\left(x+3\right)}{\left(x+1\right)\left(x+3\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+3\right) agus x+1 ná \left(x+1\right)\left(x+3\right). Méadaigh \frac{3}{x+1} faoi \frac{x+3}{x+3}.
\frac{x^{2}+bx+8+3\left(x+3\right)}{\left(x+1\right)\left(x+3\right)}
Tá an t-ainmneoir céanna ag \frac{x^{2}+bx+8}{\left(x+1\right)\left(x+3\right)} agus \frac{3\left(x+3\right)}{\left(x+1\right)\left(x+3\right)} agus, mar sin, is féidir iad a shuimiú trína n-uimhreoirí a shuimiú.
\frac{x^{2}+bx+8+3x+9}{\left(x+1\right)\left(x+3\right)}
Déan iolrúcháin in x^{2}+bx+8+3\left(x+3\right).
\frac{x^{2}+bx+17+3x}{\left(x+1\right)\left(x+3\right)}
Cumaisc téarmaí comhchosúla in: x^{2}+bx+8+3x+9.
\frac{x^{2}+bx+17+3x}{x^{2}+4x+3}
Fairsingigh \left(x+1\right)\left(x+3\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}