Solve (x-8)/(frac{x{8}-8/x)}

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

Evaluate

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

Short Solution Steps

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

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

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

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

Do the multiplications in xx-8\times 8.

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

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

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

Factor the expressions that are not already factored.

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

Cancel out x-8 in both numerator and denominator.

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

Expand

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

Short Solution Steps

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

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

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

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

Do the multiplications in xx-8\times 8.

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

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

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

Factor the expressions that are not already factored.

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

Cancel out x-8 in both numerator and denominator.

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