Solve 2x-8x^-1/8x^-3+2x^-1-1

$$\frac{ 2x-8 { x }^{ -1 } }{ 8 { x }^{ -3 } +2 { x }^{ -1 } -1 }$$

Evaluate

$$-\frac{2x^{2}\left(x^{2}-4\right)}{x^{3}-2x^{2}-8}$$

Short Solution Steps

Factor the expressions that are not already factored.

$$\frac{2\times \frac{1}{x}\left(x-2\right)\left(x+2\right)}{-x^{-3}\left(x^{3}-2x^{2}-8\right)}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent.

$$\frac{2\left(x-2\right)\left(x+2\right)x^{2}}{-\left(x^{3}-2x^{2}-8\right)}$$

Expand the expression.

$$\frac{2x^{4}-8x^{2}}{-x^{3}+2x^{2}+8}$$

Expand

$$\frac{2\left(x^{4}-4x^{2}\right)}{8+2x^{2}-x^{3}}$$

Short Solution Steps

Factor the expressions that are not already factored.

$$\frac{2\times \frac{1}{x}\left(x-2\right)\left(x+2\right)}{-x^{-3}\left(x^{3}-2x^{2}-8\right)}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent.

$$\frac{2\left(x-2\right)\left(x+2\right)x^{2}}{-\left(x^{3}-2x^{2}-8\right)}$$

Expand the expression.

$$\frac{2x^{4}-8x^{2}}{-x^{3}+2x^{2}+8}$$