Simplify 1/(x+h)-1/x

$\frac{1}{x + h} - \frac{1}{x}$

Step 1

To write $\frac{1}{x + h}$ as a fraction with a common denominator, multiply by $\frac{x}{x}$ .

$\frac{1}{x + h} \cdot \frac{x}{x} - \frac{1}{x}$

Step 2

To write $- \frac{1}{x}$ as a fraction with a common denominator, multiply by $\frac{x + h}{x + h}$ .

$\frac{1}{x + h} \cdot \frac{x}{x} - \frac{1}{x} \cdot \frac{x + h}{x + h}$

Step 3

Write each expression with a common denominator of $(x + h) x$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{1}{x + h}$ by $\frac{x}{x}$ .

$\frac{x}{(x + h) x} - \frac{1}{x} \cdot \frac{x + h}{x + h}$

Multiply $\frac{1}{x}$ by $\frac{x + h}{x + h}$ .

$\frac{x}{(x + h) x} - \frac{x + h}{x (x + h)}$

Reorder the factors of $(x + h) x$ .

$\frac{x}{x (x + h)} - \frac{x + h}{x (x + h)}$

Step 4

Combine the numerators over the common denominator.

$\frac{x - (x + h)}{x (x + h)}$

Step 5

Simplify the numerator.

Apply the distributive property.

$\frac{x - x - h}{x (x + h)}$

Subtract $x$ from $x$ .

$\frac{0 - h}{x (x + h)}$

Subtract $h$ from $0$ .

$\frac{- h}{x (x + h)}$

Step 6

Move the negative in front of the fraction.

$- \frac{h}{x (x + h)}$