Solve x-18/x-7/1-frac{2{x-7}}

$$\frac { x - \frac { 18 } { x - 7 } } { 1 - \frac { 2 } { x - 7 } }$$

Evaluate

$$x+2$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply x times \frac{x-7}{x-7}.

$$\frac{\frac{x\left(x-7\right)}{x-7}-\frac{18}{x-7}}{1-\frac{2}{x-7}}$$

Since \frac{x\left(x-7\right)}{x-7} and \frac{18}{x-7} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{x\left(x-7\right)-18}{x-7}}{1-\frac{2}{x-7}}$$

Do the multiplications in x\left(x-7\right)-18.

$$\frac{\frac{x^{2}-7x-18}{x-7}}{1-\frac{2}{x-7}}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{x-7}{x-7}.

$$\frac{\frac{x^{2}-7x-18}{x-7}}{\frac{x-7}{x-7}-\frac{2}{x-7}}$$

Since \frac{x-7}{x-7} and \frac{2}{x-7} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{x^{2}-7x-18}{x-7}}{\frac{x-7-2}{x-7}}$$

Combine like terms in x-7-2.

$$\frac{\frac{x^{2}-7x-18}{x-7}}{\frac{x-9}{x-7}}$$

Divide \frac{x^{2}-7x-18}{x-7} by \frac{x-9}{x-7} by multiplying \frac{x^{2}-7x-18}{x-7} by the reciprocal of \frac{x-9}{x-7}.

$$\frac{\left(x^{2}-7x-18\right)\left(x-7\right)}{\left(x-7\right)\left(x-9\right)}$$

Cancel out x-7 in both numerator and denominator.

$$\frac{x^{2}-7x-18}{x-9}$$

Factor the expressions that are not already factored.

$$\frac{\left(x-9\right)\left(x+2\right)}{x-9}$$

Cancel out x-9 in both numerator and denominator.

$$x+2$$

Expand

$$x+2$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply x times \frac{x-7}{x-7}.

$$\frac{\frac{x\left(x-7\right)}{x-7}-\frac{18}{x-7}}{1-\frac{2}{x-7}}$$

Since \frac{x\left(x-7\right)}{x-7} and \frac{18}{x-7} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{x\left(x-7\right)-18}{x-7}}{1-\frac{2}{x-7}}$$

Do the multiplications in x\left(x-7\right)-18.

$$\frac{\frac{x^{2}-7x-18}{x-7}}{1-\frac{2}{x-7}}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{x-7}{x-7}.

$$\frac{\frac{x^{2}-7x-18}{x-7}}{\frac{x-7}{x-7}-\frac{2}{x-7}}$$

Since \frac{x-7}{x-7} and \frac{2}{x-7} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{x^{2}-7x-18}{x-7}}{\frac{x-7-2}{x-7}}$$

Combine like terms in x-7-2.

$$\frac{\frac{x^{2}-7x-18}{x-7}}{\frac{x-9}{x-7}}$$

Divide \frac{x^{2}-7x-18}{x-7} by \frac{x-9}{x-7} by multiplying \frac{x^{2}-7x-18}{x-7} by the reciprocal of \frac{x-9}{x-7}.

$$\frac{\left(x^{2}-7x-18\right)\left(x-7\right)}{\left(x-7\right)\left(x-9\right)}$$

Cancel out x-7 in both numerator and denominator.

$$\frac{x^{2}-7x-18}{x-9}$$

Factor the expressions that are not already factored.

$$\frac{\left(x-9\right)\left(x+2\right)}{x-9}$$

Cancel out x-9 in both numerator and denominator.

$$x+2$$