Solve x+8/x-6/1-frac{2{x}}

$$\frac { x + \frac { 8 } { x - 6 } } { 1 - \frac { 2 } { x } }$$

Evaluate

$$\frac{x\left(x-4\right)}{x-6}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply x times \frac{x-6}{x-6}.

$$\frac{\frac{x\left(x-6\right)}{x-6}+\frac{8}{x-6}}{1-\frac{2}{x}}$$

Since \frac{x\left(x-6\right)}{x-6} and \frac{8}{x-6} have the same denominator, add them by adding their numerators.

$$\frac{\frac{x\left(x-6\right)+8}{x-6}}{1-\frac{2}{x}}$$

Do the multiplications in x\left(x-6\right)+8.

$$\frac{\frac{x^{2}-6x+8}{x-6}}{1-\frac{2}{x}}$$

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

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

Since \frac{x}{x} and \frac{2}{x} have the same denominator, subtract them by subtracting their numerators.

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

Divide \frac{x^{2}-6x+8}{x-6} by \frac{x-2}{x} by multiplying \frac{x^{2}-6x+8}{x-6} by the reciprocal of \frac{x-2}{x}.

$$\frac{\left(x^{2}-6x+8\right)x}{\left(x-6\right)\left(x-2\right)}$$

Factor the expressions that are not already factored.

$$\frac{x\left(x-4\right)\left(x-2\right)}{\left(x-6\right)\left(x-2\right)}$$

Cancel out x-2 in both numerator and denominator.

$$\frac{x\left(x-4\right)}{x-6}$$

Expand the expression.

$$\frac{x^{2}-4x}{x-6}$$

Expand

$$\frac{x^{2}-4x}{x-6}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply x times \frac{x-6}{x-6}.

$$\frac{\frac{x\left(x-6\right)}{x-6}+\frac{8}{x-6}}{1-\frac{2}{x}}$$

Since \frac{x\left(x-6\right)}{x-6} and \frac{8}{x-6} have the same denominator, add them by adding their numerators.

$$\frac{\frac{x\left(x-6\right)+8}{x-6}}{1-\frac{2}{x}}$$

Do the multiplications in x\left(x-6\right)+8.

$$\frac{\frac{x^{2}-6x+8}{x-6}}{1-\frac{2}{x}}$$

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

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

Since \frac{x}{x} and \frac{2}{x} have the same denominator, subtract them by subtracting their numerators.

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

Divide \frac{x^{2}-6x+8}{x-6} by \frac{x-2}{x} by multiplying \frac{x^{2}-6x+8}{x-6} by the reciprocal of \frac{x-2}{x}.

$$\frac{\left(x^{2}-6x+8\right)x}{\left(x-6\right)\left(x-2\right)}$$

Factor the expressions that are not already factored.

$$\frac{x\left(x-4\right)\left(x-2\right)}{\left(x-6\right)\left(x-2\right)}$$

Cancel out x-2 in both numerator and denominator.

$$\frac{x\left(x-4\right)}{x-6}$$

Expand the expression.

$$\frac{x^{2}-4x}{x-6}$$