Solve frac{frac{x^{3}}{x^2-4}}{x^3-7x^2/x^2+5x-14}

$$\frac { \frac { x ^ { 3 } } { x ^ { 2 } - 4 } } { \frac { x ^ { 3 } - 7 x ^ { 2 } } { x ^ { 2 } + 5 x - 14 } }$$

Evaluate

$$\frac{x\left(x+7\right)}{\left(x-7\right)\left(x+2\right)}$$

Short Solution Steps

Divide \frac{x^{3}}{x^{2}-4} by \frac{x^{3}-7x^{2}}{x^{2}+5x-14} by multiplying \frac{x^{3}}{x^{2}-4} by the reciprocal of \frac{x^{3}-7x^{2}}{x^{2}+5x-14}.

$$\frac{x^{3}\left(x^{2}+5x-14\right)}{\left(x^{2}-4\right)\left(x^{3}-7x^{2}\right)}$$

Factor the expressions that are not already factored.

$$\frac{\left(x-2\right)\left(x+7\right)x^{3}}{\left(x-7\right)\left(x-2\right)\left(x+2\right)x^{2}}$$

Cancel out \left(x-2\right)x^{2} in both numerator and denominator.

$$\frac{x\left(x+7\right)}{\left(x-7\right)\left(x+2\right)}$$

Expand the expression.

$$\frac{x^{2}+7x}{x^{2}-5x-14}$$

Expand

$$\frac{x^{2}+7x}{\left(x-7\right)\left(x+2\right)}$$

Short Solution Steps

Divide \frac{x^{3}}{x^{2}-4} by \frac{x^{3}-7x^{2}}{x^{2}+5x-14} by multiplying \frac{x^{3}}{x^{2}-4} by the reciprocal of \frac{x^{3}-7x^{2}}{x^{2}+5x-14}.

$$\frac{x^{3}\left(x^{2}+5x-14\right)}{\left(x^{2}-4\right)\left(x^{3}-7x^{2}\right)}$$

Factor the expressions that are not already factored.

$$\frac{\left(x-2\right)\left(x+7\right)x^{3}}{\left(x-7\right)\left(x-2\right)\left(x+2\right)x^{2}}$$

Cancel out \left(x-2\right)x^{2} in both numerator and denominator.

$$\frac{x\left(x+7\right)}{\left(x-7\right)\left(x+2\right)}$$

Expand the expression.

$$\frac{x^{2}+7x}{x^{2}-5x-14}$$