Solve (1/y-1/x+y):x/y

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

Evaluate

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

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of y and x+y is y\left(x+y\right). Multiply \frac{1}{y} times \frac{x+y}{x+y}. Multiply \frac{1}{x+y} times \frac{y}{y}.

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

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

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

Combine like terms in x+y-y.

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

Divide \frac{x}{y\left(x+y\right)} by \frac{x}{y} by multiplying \frac{x}{y\left(x+y\right)} by the reciprocal of \frac{x}{y}.

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

Cancel out xy in both numerator and denominator.

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

Expand

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

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of y and x+y is y\left(x+y\right). Multiply \frac{1}{y} times \frac{x+y}{x+y}. Multiply \frac{1}{x+y} times \frac{y}{y}.

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

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

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

Combine like terms in x+y-y.

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

Divide \frac{x}{y\left(x+y\right)} by \frac{x}{y} by multiplying \frac{x}{y\left(x+y\right)} by the reciprocal of \frac{x}{y}.

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

Cancel out xy in both numerator and denominator.

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