Solve 10/5+h-10/5/5+h-5

$$\frac { \frac { 10 } { 5 + h } - \frac { 10 } { 5 } } { 5 + h - 5 }$$

Evaluate

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

Short Solution Steps

Divide 10 by 5 to get 2.

$$\frac{\frac{10}{5+h}-2}{5+h-5}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 2 times \frac{5+h}{5+h}.

$$\frac{\frac{10}{5+h}-\frac{2\left(5+h\right)}{5+h}}{5+h-5}$$

Since \frac{10}{5+h} and \frac{2\left(5+h\right)}{5+h} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{10-2\left(5+h\right)}{5+h}}{5+h-5}$$

Do the multiplications in 10-2\left(5+h\right).

$$\frac{\frac{10-10-2h}{5+h}}{5+h-5}$$

Combine like terms in 10-10-2h.

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

Subtract 5 from 5 to get 0.

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

Express \frac{\frac{-2h}{5+h}}{h} as a single fraction.

$$\frac{-2h}{\left(5+h\right)h}$$

Cancel out h in both numerator and denominator.

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

Expand

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

Short Solution Steps

Divide 10 by 5 to get 2.

$$\frac{\frac{10}{5+h}-2}{5+h-5}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 2 times \frac{5+h}{5+h}.

$$\frac{\frac{10}{5+h}-\frac{2\left(5+h\right)}{5+h}}{5+h-5}$$

Since \frac{10}{5+h} and \frac{2\left(5+h\right)}{5+h} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{10-2\left(5+h\right)}{5+h}}{5+h-5}$$

Do the multiplications in 10-2\left(5+h\right).

$$\frac{\frac{10-10-2h}{5+h}}{5+h-5}$$

Combine like terms in 10-10-2h.

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

Subtract 5 from 5 to get 0.

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

Express \frac{\frac{-2h}{5+h}}{h} as a single fraction.

$$\frac{-2h}{\left(5+h\right)h}$$

Cancel out h in both numerator and denominator.

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