Solve x^2-x-2/1/frac{1{x^2-4}}

$$\frac { \frac { x ^ { 2 } - x - 2 } { 1 } } { \frac { 1 } { x ^ { 2 } - 4 } }$$

Evaluate

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

Solution Steps

Divide \frac{x^{2}-x-2}{1} by \frac{1}{x^{2}-4} by multiplying \frac{x^{2}-x-2}{1} by the reciprocal of \frac{1}{x^{2}-4}.

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

Use the distributive property to multiply x^{2}-x-2 by x^{2}-4 and combine like terms.

$$x^{4}-6x^{2}-x^{3}+4x+8$$

Expand

$$x^{4}-x^{3}-6x^{2}+4x+8$$

Solution Steps

Divide \frac{x^{2}-x-2}{1} by \frac{1}{x^{2}-4} by multiplying \frac{x^{2}-x-2}{1} by the reciprocal of \frac{1}{x^{2}-4}.

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

Use the distributive property to multiply x^{2}-x-2 by x^{2}-4 and combine like terms.

$$x^{4}-6x^{2}-x^{3}+4x+8$$