Solve 4/x+h-4/h

$$\frac { 4 } { x + h } - \frac { 4 } { h }$$

Evaluate

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

Short Solution Steps

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

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

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

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

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

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

Combine like terms in 4h-4x-4h.

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

Expand h\left(x+h\right).

$$\frac{-4x}{hx+h^{2}}$$

Factor

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