Solve x+9/x-10/1-frac{1{x}}

$$\frac { x + \frac { 9 } { x - 10 } } { 1 - \frac { 1 } { x } }$$

Evaluate

$$\frac{x\left(x-9\right)}{x-10}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply x times \frac{x-10}{x-10}.

$$\frac{\frac{x\left(x-10\right)}{x-10}+\frac{9}{x-10}}{1-\frac{1}{x}}$$

Since \frac{x\left(x-10\right)}{x-10} and \frac{9}{x-10} have the same denominator, add them by adding their numerators.

$$\frac{\frac{x\left(x-10\right)+9}{x-10}}{1-\frac{1}{x}}$$

Do the multiplications in x\left(x-10\right)+9.

$$\frac{\frac{x^{2}-10x+9}{x-10}}{1-\frac{1}{x}}$$

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

$$\frac{\frac{x^{2}-10x+9}{x-10}}{\frac{x}{x}-\frac{1}{x}}$$

Since \frac{x}{x} and \frac{1}{x} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{x^{2}-10x+9}{x-10}}{\frac{x-1}{x}}$$

Divide \frac{x^{2}-10x+9}{x-10} by \frac{x-1}{x} by multiplying \frac{x^{2}-10x+9}{x-10} by the reciprocal of \frac{x-1}{x}.

$$\frac{\left(x^{2}-10x+9\right)x}{\left(x-10\right)\left(x-1\right)}$$

Factor the expressions that are not already factored.

$$\frac{x\left(x-9\right)\left(x-1\right)}{\left(x-10\right)\left(x-1\right)}$$

Cancel out x-1 in both numerator and denominator.

$$\frac{x\left(x-9\right)}{x-10}$$

Expand the expression.

$$\frac{x^{2}-9x}{x-10}$$

Expand

$$\frac{x^{2}-9x}{x-10}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply x times \frac{x-10}{x-10}.

$$\frac{\frac{x\left(x-10\right)}{x-10}+\frac{9}{x-10}}{1-\frac{1}{x}}$$

Since \frac{x\left(x-10\right)}{x-10} and \frac{9}{x-10} have the same denominator, add them by adding their numerators.

$$\frac{\frac{x\left(x-10\right)+9}{x-10}}{1-\frac{1}{x}}$$

Do the multiplications in x\left(x-10\right)+9.

$$\frac{\frac{x^{2}-10x+9}{x-10}}{1-\frac{1}{x}}$$

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

$$\frac{\frac{x^{2}-10x+9}{x-10}}{\frac{x}{x}-\frac{1}{x}}$$

Since \frac{x}{x} and \frac{1}{x} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{x^{2}-10x+9}{x-10}}{\frac{x-1}{x}}$$

Divide \frac{x^{2}-10x+9}{x-10} by \frac{x-1}{x} by multiplying \frac{x^{2}-10x+9}{x-10} by the reciprocal of \frac{x-1}{x}.

$$\frac{\left(x^{2}-10x+9\right)x}{\left(x-10\right)\left(x-1\right)}$$

Factor the expressions that are not already factored.

$$\frac{x\left(x-9\right)\left(x-1\right)}{\left(x-10\right)\left(x-1\right)}$$

Cancel out x-1 in both numerator and denominator.

$$\frac{x\left(x-9\right)}{x-10}$$

Expand the expression.

$$\frac{x^{2}-9x}{x-10}$$