Solve 2/x-y-2/y

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

Evaluate

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

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x-y and y is y\left(x-y\right). Multiply \frac{2}{x-y} times \frac{y}{y}. Multiply \frac{2}{y} times \frac{x-y}{x-y}.

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

Since \frac{2y}{y\left(x-y\right)} and \frac{2\left(x-y\right)}{y\left(x-y\right)} have the same denominator, subtract them by subtracting their numerators.

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

Do the multiplications in 2y-2\left(x-y\right).

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

Combine like terms in 2y-2x+2y.

$$\frac{4y-2x}{y\left(x-y\right)}$$

Expand y\left(x-y\right).

$$\frac{4y-2x}{xy-y^{2}}$$

Factor

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