Evaluate
\frac{2x^{2}+x+3}{\left(x-1\right)\left(x+1\right)^{2}}
Differentiate w.r.t. x
\frac{2\left(1-6x-x^{3}\right)}{\left(x-1\right)^{2}\left(x+1\right)^{3}}
Graph
Share
Copied to clipboard
\frac{3}{\left(x-1\right)\left(x+1\right)}+\frac{2x}{\left(x+1\right)^{2}}
Factor x^{2}-1. Factor x^{2}+2x+1.
\frac{3\left(x+1\right)}{\left(x-1\right)\left(x+1\right)^{2}}+\frac{2x\left(x-1\right)}{\left(x-1\right)\left(x+1\right)^{2}}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of \left(x-1\right)\left(x+1\right) and \left(x+1\right)^{2} is \left(x-1\right)\left(x+1\right)^{2}. Multiply \frac{3}{\left(x-1\right)\left(x+1\right)} times \frac{x+1}{x+1}. Multiply \frac{2x}{\left(x+1\right)^{2}} times \frac{x-1}{x-1}.
\frac{3\left(x+1\right)+2x\left(x-1\right)}{\left(x-1\right)\left(x+1\right)^{2}}
Since \frac{3\left(x+1\right)}{\left(x-1\right)\left(x+1\right)^{2}} and \frac{2x\left(x-1\right)}{\left(x-1\right)\left(x+1\right)^{2}} have the same denominator, add them by adding their numerators.
\frac{3x+3+2x^{2}-2x}{\left(x-1\right)\left(x+1\right)^{2}}
Do the multiplications in 3\left(x+1\right)+2x\left(x-1\right).
\frac{x+3+2x^{2}}{\left(x-1\right)\left(x+1\right)^{2}}
Combine like terms in 3x+3+2x^{2}-2x.
\frac{x+3+2x^{2}}{x^{3}+x^{2}-x-1}
Expand \left(x-1\right)\left(x+1\right)^{2}.
Examples
Quadratic equation
{ x } ^ { 2 } - 4 x - 5 = 0
Trigonometry
4 \sin \theta \cos \theta = 2 \sin \theta
Linear equation
y = 3x + 4
Arithmetic
699 * 533
Matrix
\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]
Simultaneous equation
\left. \begin{cases} { 8x+2y = 46 } \\ { 7x+3y = 47 } \end{cases} \right.
Differentiation
\frac { d } { d x } \frac { ( 3 x ^ { 2 } - 2 ) } { ( x - 5 ) }
Integration
\int _ { 0 } ^ { 1 } x e ^ { - x ^ { 2 } } d x
Limits
\lim _{x \rightarrow-3} \frac{x^{2}-9}{x^{2}+2 x-3}