Solve x^2-4/x^2-x-2div3x+6/x^2+x

$$\frac { x ^ { 2 } - 4 } { x ^ { 2 } - x - 2 } \div \frac { 3 x + 6 } { x ^ { 2 } + x }$$

Evaluate

$$\frac{x}{3}$$

Short Solution Steps

Divide \frac{x^{2}-4}{x^{2}-x-2} by \frac{3x+6}{x^{2}+x} by multiplying \frac{x^{2}-4}{x^{2}-x-2} by the reciprocal of \frac{3x+6}{x^{2}+x}.

$$\frac{\left(x^{2}-4\right)\left(x^{2}+x\right)}{\left(x^{2}-x-2\right)\left(3x+6\right)}$$

Factor the expressions that are not already factored.

$$\frac{x\left(x-2\right)\left(x+1\right)\left(x+2\right)}{3\left(x-2\right)\left(x+1\right)\left(x+2\right)}$$

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

$$\frac{x}{3}$$

Expand

$$\frac{x}{3}$$

Short Solution Steps

Divide \frac{x^{2}-4}{x^{2}-x-2} by \frac{3x+6}{x^{2}+x} by multiplying \frac{x^{2}-4}{x^{2}-x-2} by the reciprocal of \frac{3x+6}{x^{2}+x}.

$$\frac{\left(x^{2}-4\right)\left(x^{2}+x\right)}{\left(x^{2}-x-2\right)\left(3x+6\right)}$$

Factor the expressions that are not already factored.

$$\frac{x\left(x-2\right)\left(x+1\right)\left(x+2\right)}{3\left(x-2\right)\left(x+1\right)\left(x+2\right)}$$

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

$$\frac{x}{3}$$