Solve 5/5+h-5/h

$$\frac { \frac { 5 } { 5 + h } - 5 } { h }$$

Evaluate

$$-\frac{5\left(h+4\right)}{h\left(h+5\right)}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 5 times \frac{5+h}{5+h}.

$$\frac{\frac{5}{5+h}-\frac{5\left(5+h\right)}{5+h}}{h}$$

Since \frac{5}{5+h} and \frac{5\left(5+h\right)}{5+h} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{5-5\left(5+h\right)}{5+h}}{h}$$

Do the multiplications in 5-5\left(5+h\right).

$$\frac{\frac{5-25-5h}{5+h}}{h}$$

Combine like terms in 5-25-5h.

$$\frac{\frac{-20-5h}{5+h}}{h}$$

Express \frac{\frac{-20-5h}{5+h}}{h} as a single fraction.

$$\frac{-20-5h}{\left(5+h\right)h}$$

Use the distributive property to multiply 5+h by h.

$$\frac{-20-5h}{5h+h^{2}}$$

Expand

$$-\frac{5\left(h+4\right)}{h\left(h+5\right)}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 5 times \frac{5+h}{5+h}.

$$\frac{\frac{5}{5+h}-\frac{5\left(5+h\right)}{5+h}}{h}$$

Since \frac{5}{5+h} and \frac{5\left(5+h\right)}{5+h} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{5-5\left(5+h\right)}{5+h}}{h}$$

Do the multiplications in 5-5\left(5+h\right).

$$\frac{\frac{5-25-5h}{5+h}}{h}$$

Combine like terms in 5-25-5h.

$$\frac{\frac{-20-5h}{5+h}}{h}$$

Express \frac{\frac{-20-5h}{5+h}}{h} as a single fraction.

$$\frac{-20-5h}{\left(5+h\right)h}$$

Use the distributive property to multiply 5+h by h.

$$\frac{-20-5h}{5h+h^{2}}$$