Evaluate
-\frac{\left(x+1\right)\left(x+3\right)}{2x^{2}}
Expand
-\frac{1}{2}-\frac{2}{x}-\frac{3}{2x^{2}}
Graph
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\frac{\left(2-x\right)\left(x^{2}+2x+1\right)}{\left(x^{2}+x\right)\left(x^{2}-3x\right)}\times \frac{9-x^{2}}{4-2x}
Divide \frac{2-x}{x^{2}+x} by \frac{x^{2}-3x}{x^{2}+2x+1} by multiplying \frac{2-x}{x^{2}+x} by the reciprocal of \frac{x^{2}-3x}{x^{2}+2x+1}.
\frac{\left(-x+2\right)\left(x+1\right)^{2}}{\left(x-3\right)\left(x+1\right)x^{2}}\times \frac{9-x^{2}}{4-2x}
Factor the expressions that are not already factored in \frac{\left(2-x\right)\left(x^{2}+2x+1\right)}{\left(x^{2}+x\right)\left(x^{2}-3x\right)}.
\frac{\left(x+1\right)\left(-x+2\right)}{\left(x-3\right)x^{2}}\times \frac{9-x^{2}}{4-2x}
Cancel out x+1 in both numerator and denominator.
\frac{\left(x+1\right)\left(-x+2\right)\left(9-x^{2}\right)}{\left(x-3\right)x^{2}\left(4-2x\right)}
Multiply \frac{\left(x+1\right)\left(-x+2\right)}{\left(x-3\right)x^{2}} times \frac{9-x^{2}}{4-2x} by multiplying numerator times numerator and denominator times denominator.
\frac{\left(x-3\right)\left(-x-3\right)\left(x+1\right)\left(-x+2\right)}{2\left(x-3\right)\left(-x+2\right)x^{2}}
Factor the expressions that are not already factored.
\frac{\left(-x-3\right)\left(x+1\right)}{2x^{2}}
Cancel out \left(x-3\right)\left(-x+2\right) in both numerator and denominator.
\frac{-x^{2}-4x-3}{2x^{2}}
Expand the expression.
\frac{\left(2-x\right)\left(x^{2}+2x+1\right)}{\left(x^{2}+x\right)\left(x^{2}-3x\right)}\times \frac{9-x^{2}}{4-2x}
Divide \frac{2-x}{x^{2}+x} by \frac{x^{2}-3x}{x^{2}+2x+1} by multiplying \frac{2-x}{x^{2}+x} by the reciprocal of \frac{x^{2}-3x}{x^{2}+2x+1}.
\frac{\left(-x+2\right)\left(x+1\right)^{2}}{\left(x-3\right)\left(x+1\right)x^{2}}\times \frac{9-x^{2}}{4-2x}
Factor the expressions that are not already factored in \frac{\left(2-x\right)\left(x^{2}+2x+1\right)}{\left(x^{2}+x\right)\left(x^{2}-3x\right)}.
\frac{\left(x+1\right)\left(-x+2\right)}{\left(x-3\right)x^{2}}\times \frac{9-x^{2}}{4-2x}
Cancel out x+1 in both numerator and denominator.
\frac{\left(x+1\right)\left(-x+2\right)\left(9-x^{2}\right)}{\left(x-3\right)x^{2}\left(4-2x\right)}
Multiply \frac{\left(x+1\right)\left(-x+2\right)}{\left(x-3\right)x^{2}} times \frac{9-x^{2}}{4-2x} by multiplying numerator times numerator and denominator times denominator.
\frac{\left(x-3\right)\left(-x-3\right)\left(x+1\right)\left(-x+2\right)}{2\left(x-3\right)\left(-x+2\right)x^{2}}
Factor the expressions that are not already factored.
\frac{\left(-x-3\right)\left(x+1\right)}{2x^{2}}
Cancel out \left(x-3\right)\left(-x+2\right) in both numerator and denominator.
\frac{-x^{2}-4x-3}{2x^{2}}
Expand the expression.
Examples
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{ 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}