Solve 1+1/x/1-frac{x{y}}

$$\frac { 1 + \frac { 1 } { x } } { 1 - \frac { x } { y } }$$

Evaluate

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

Short Solution Steps

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

$$\frac{\frac{x}{x}+\frac{1}{x}}{1-\frac{x}{y}}$$

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

$$\frac{\frac{x+1}{x}}{1-\frac{x}{y}}$$

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

$$\frac{\frac{x+1}{x}}{\frac{y}{y}-\frac{x}{y}}$$

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

$$\frac{\frac{x+1}{x}}{\frac{y-x}{y}}$$

Divide \frac{x+1}{x} by \frac{y-x}{y} by multiplying \frac{x+1}{x} by the reciprocal of \frac{y-x}{y}.

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

Use the distributive property to multiply x+1 by y.

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

Use the distributive property to multiply x by y-x.

$$\frac{xy+y}{xy-x^{2}}$$

Expand

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

Short Solution Steps

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

$$\frac{\frac{x}{x}+\frac{1}{x}}{1-\frac{x}{y}}$$

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

$$\frac{\frac{x+1}{x}}{1-\frac{x}{y}}$$

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

$$\frac{\frac{x+1}{x}}{\frac{y}{y}-\frac{x}{y}}$$

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

$$\frac{\frac{x+1}{x}}{\frac{y-x}{y}}$$

Divide \frac{x+1}{x} by \frac{y-x}{y} by multiplying \frac{x+1}{x} by the reciprocal of \frac{y-x}{y}.

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

Use the distributive property to multiply x+1 by y.

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

Use the distributive property to multiply x by y-x.

$$\frac{xy+y}{xy-x^{2}}$$