Simplify (1/(x+4)-1/x)/4

$\frac{\frac{1}{x + 4} - \frac{1}{x}}{4}$

Simplify the numerator.

To write $\frac{1}{x + 4}$ as a fraction with a common denominator, multiply by $\frac{x}{x}$ .

$\frac{\frac{1}{x + 4} \cdot \frac{x}{x} - \frac{1}{x}}{4}$

To write $- \frac{1}{x}$ as a fraction with a common denominator, multiply by $\frac{x + 4}{x + 4}$ .

$\frac{\frac{1}{x + 4} \cdot \frac{x}{x} - \frac{1}{x} \cdot \frac{x + 4}{x + 4}}{4}$

Write each expression with a common denominator of $(x + 4) x$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{1}{x + 4}$ by $\frac{x}{x}$ .

$\frac{\frac{x}{(x + 4) x} - \frac{1}{x} \cdot \frac{x + 4}{x + 4}}{4}$

Multiply $\frac{1}{x}$ by $\frac{x + 4}{x + 4}$ .

$\frac{\frac{x}{(x + 4) x} - \frac{x + 4}{x (x + 4)}}{4}$

Reorder the factors of $(x + 4) x$ .

$\frac{\frac{x}{x (x + 4)} - \frac{x + 4}{x (x + 4)}}{4}$

Combine the numerators over the common denominator.

$\frac{\frac{x - (x + 4)}{x (x + 4)}}{4}$

Rewrite $\frac{x - (x + 4)}{x (x + 4)}$ in a factored form.

Apply the distributive property.

$\frac{\frac{x - x - 1 \cdot 4}{x (x + 4)}}{4}$

Multiply $- 1$ by $4$ .

$\frac{\frac{x - x - 4}{x (x + 4)}}{4}$

Subtract $x$ from $x$ .

$\frac{\frac{0 - 4}{x (x + 4)}}{4}$

Subtract $4$ from $0$ .

$\frac{\frac{- 4}{x (x + 4)}}{4}$

Move the negative in front of the fraction.

$\frac{- \frac{4}{x (x + 4)}}{4}$

Multiply the numerator by the reciprocal of the denominator.

$- \frac{4}{x (x + 4)} \cdot \frac{1}{4}$

Cancel the common factor of $4$ .

Move the leading negative in $- \frac{4}{x (x + 4)}$ into the numerator.

$\frac{- 4}{x (x + 4)} \cdot \frac{1}{4}$

Factor $4$ out of $- 4$ .

$\frac{4 (- 1)}{x (x + 4)} \cdot \frac{1}{4}$

Cancel the common factor.

$\frac{4 \cdot - 1}{x (x + 4)} \cdot \frac{1}{4}$

Rewrite the expression.

$\frac{- 1}{x (x + 4)}$

Move the negative in front of the fraction.

$- \frac{1}{x (x + 4)}$