Solve 4/x-y-4/x

$$\frac{ 4 }{ x-y } - \frac{ 4 }{ x }$$

Evaluate

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

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x-y and x is x\left(x-y\right). Multiply \frac{4}{x-y} times \frac{x}{x}. Multiply \frac{4}{x} times \frac{x-y}{x-y}.

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

Since \frac{4x}{x\left(x-y\right)} and \frac{4\left(x-y\right)}{x\left(x-y\right)} have the same denominator, subtract them by subtracting their numerators.

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

Do the multiplications in 4x-4\left(x-y\right).

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

Combine like terms in 4x-4x+4y.

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

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

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

Factor

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