Solve +x-8/x-2/frac{x{4}-1}

$$\frac { + \frac { x - 8 } { x - 2 } } { \frac { x } { 4 } - 1 }$$

Evaluate

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

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{4}{4}.

$$\frac{\frac{x-8}{x-2}}{\frac{x}{4}-\frac{4}{4}}$$

Since \frac{x}{4} and \frac{4}{4} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{x-8}{x-2}}{\frac{x-4}{4}}$$

Divide \frac{x-8}{x-2} by \frac{x-4}{4} by multiplying \frac{x-8}{x-2} by the reciprocal of \frac{x-4}{4}.

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

Use the distributive property to multiply x-8 by 4.

$$\frac{4x-32}{\left(x-2\right)\left(x-4\right)}$$

Apply the distributive property by multiplying each term of x-2 by each term of x-4.

$$\frac{4x-32}{x^{2}-4x-2x+8}$$

Combine -4x and -2x to get -6x.

$$\frac{4x-32}{x^{2}-6x+8}$$

Expand

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

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{4}{4}.

$$\frac{\frac{x-8}{x-2}}{\frac{x}{4}-\frac{4}{4}}$$

Since \frac{x}{4} and \frac{4}{4} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{x-8}{x-2}}{\frac{x-4}{4}}$$

Divide \frac{x-8}{x-2} by \frac{x-4}{4} by multiplying \frac{x-8}{x-2} by the reciprocal of \frac{x-4}{4}.

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

Use the distributive property to multiply x-8 by 4.

$$\frac{4x-32}{\left(x-2\right)\left(x-4\right)}$$

Apply the distributive property by multiplying each term of x-2 by each term of x-4.

$$\frac{4x-32}{x^{2}-4x-2x+8}$$

Combine -4x and -2x to get -6x.

$$\frac{4x-32}{x^{2}-6x+8}$$