Solve 8/x^2-8x-x/8x-64

$$\frac { 8 } { x ^ { 2 } - 8 x } - \frac { x } { 8 x - 64 }$$

Evaluate

$$-\frac{1}{8}-\frac{1}{x}$$

Short Solution Steps

Factor x^{2}-8x. Factor 8x-64.

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

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x\left(x-8\right) and 8\left(x-8\right) is 8x\left(x-8\right). Multiply \frac{8}{x\left(x-8\right)} times \frac{8}{8}. Multiply \frac{x}{8\left(x-8\right)} times \frac{x}{x}.

$$\frac{8\times 8}{8x\left(x-8\right)}-\frac{xx}{8x\left(x-8\right)}$$

Since \frac{8\times 8}{8x\left(x-8\right)} and \frac{xx}{8x\left(x-8\right)} have the same denominator, subtract them by subtracting their numerators.

$$\frac{8\times 8-xx}{8x\left(x-8\right)}$$

Do the multiplications in 8\times 8-xx.

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

Factor the expressions that are not already factored in \frac{64-x^{2}}{8x\left(x-8\right)}.

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

Cancel out x-8 in both numerator and denominator.

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

Factor

$$-\frac{\frac{1}{8}\left(x+8\right)}{x}$$