Solve (x^2-64/x)/[frac{(x-8)^2{x}]}

$$\frac { ( \frac { x ^ { 2 } - 64 } { x } ) } { [ \frac { ( x - 8 ) ^ { 2 } } { x } ] }$$

Evaluate

$$\frac{x+8}{x-8}$$

Short Solution Steps

Divide \frac{x^{2}-64}{x} by \frac{\left(x-8\right)^{2}}{x} by multiplying \frac{x^{2}-64}{x} by the reciprocal of \frac{\left(x-8\right)^{2}}{x}.

$$\frac{\left(x^{2}-64\right)x}{x\left(x-8\right)^{2}}$$

Cancel out x in both numerator and denominator.

$$\frac{x^{2}-64}{\left(x-8\right)^{2}}$$

Factor the expressions that are not already factored.

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

Cancel out x-8 in both numerator and denominator.

$$\frac{x+8}{x-8}$$

Expand

$$\frac{x+8}{x-8}$$

Short Solution Steps

Divide \frac{x^{2}-64}{x} by \frac{\left(x-8\right)^{2}}{x} by multiplying \frac{x^{2}-64}{x} by the reciprocal of \frac{\left(x-8\right)^{2}}{x}.

$$\frac{\left(x^{2}-64\right)x}{x\left(x-8\right)^{2}}$$

Cancel out x in both numerator and denominator.

$$\frac{x^{2}-64}{\left(x-8\right)^{2}}$$

Factor the expressions that are not already factored.

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

Cancel out x-8 in both numerator and denominator.

$$\frac{x+8}{x-8}$$