Solve x^2-x-2/x^2-4divx^2+x/x^2+2x

$$\frac { x ^ { 2 } - x - 2 } { x ^ { 2 } - 4 } \div \frac { x ^ { 2 } + x } { x ^ { 2 } + 2 x }$$

Evaluate

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Short Solution Steps

Divide \frac{x^{2}-x-2}{x^{2}-4} by \frac{x^{2}+x}{x^{2}+2x} by multiplying \frac{x^{2}-x-2}{x^{2}-4} by the reciprocal of \frac{x^{2}+x}{x^{2}+2x}.

$$\frac{\left(x^{2}-x-2\right)\left(x^{2}+2x\right)}{\left(x^{2}-4\right)\left(x^{2}+x\right)}$$

Factor the expressions that are not already factored.

$$\frac{x\left(x-2\right)\left(x+1\right)\left(x+2\right)}{x\left(x-2\right)\left(x+1\right)\left(x+2\right)}$$

Cancel out x\left(x-2\right)\left(x+1\right)\left(x+2\right) in both numerator and denominator.

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Factor

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