Solve (1+y/x-y)divx/x^2-y^2

$$( 1 + \frac { y } { x - y } ) \div \frac { x } { x ^ { 2 } - y ^ { 2 } }$$

Evaluate

$$x+y$$

Short Solution Steps

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

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

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

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

Combine like terms in x-y+y.

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

Divide \frac{x}{x-y} by \frac{x}{x^{2}-y^{2}} by multiplying \frac{x}{x-y} by the reciprocal of \frac{x}{x^{2}-y^{2}}.

$$\frac{x\left(x^{2}-y^{2}\right)}{\left(x-y\right)x}$$

Cancel out x in both numerator and denominator.

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

Factor the expressions that are not already factored.

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

Cancel out x-y in both numerator and denominator.

$$x+y$$

Expand

$$x+y$$

Short Solution Steps

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

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

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

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

Combine like terms in x-y+y.

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

Divide \frac{x}{x-y} by \frac{x}{x^{2}-y^{2}} by multiplying \frac{x}{x-y} by the reciprocal of \frac{x}{x^{2}-y^{2}}.

$$\frac{x\left(x^{2}-y^{2}\right)}{\left(x-y\right)x}$$

Cancel out x in both numerator and denominator.

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

Factor the expressions that are not already factored.

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

Cancel out x-y in both numerator and denominator.

$$x+y$$