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

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

Evaluate

$$\frac{xy+1}{xy-1}$$

Solution Steps

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

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

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

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

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

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

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

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

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

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

Cancel out y in both numerator and denominator.

$$\frac{xy+1}{xy-1}$$

Expand

$$\frac{xy+1}{xy-1}$$

Solution Steps

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

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

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

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

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

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

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

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

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

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

Cancel out y in both numerator and denominator.

$$\frac{xy+1}{xy-1}$$