# How do you simplify ((1/(3+h)) - (1/3)) / h?

Jan 18, 2017

Multiply by 1 in the form of $\frac{3 \left(3 + h\right)}{3 \left(3 + h\right)}$
A common factor of $\frac{h}{h}$ will cancel

#### Explanation:

Given: $\frac{\frac{1}{3 + h} - \frac{1}{3}}{h}$

Multiply by 1 in the form of $\frac{3 \left(3 + h\right)}{3 \left(3 + h\right)}$

$\frac{\frac{1}{3 + h} - \frac{1}{3}}{h} \frac{3 \left(3 + h\right)}{3 \left(3 + h\right)}$

Using the distributive property on the numerators and just multiplication on the denominator:

$\frac{\frac{3 \left(3 + h\right)}{3 + h} - \frac{3 \left(3 + h\right)}{3}}{3 h \left(3 + h\right)}$

$\frac{\frac{3 \cancel{\left(3 + h\right)}}{\cancel{\left(3 + h\right)}} - \frac{\cancel{3} \left(3 + h\right)}{\cancel{3}}}{3 h \left(3 + h\right)}$

$\frac{3 - \left(3 + h\right)}{3 h \left(3 + h\right)}$

Distribute the minus:

$\frac{3 - 3 - h}{3 h \left(3 + h\right)}$

$\frac{- h}{3 h \left(3 + h\right)}$

$\frac{h}{h}$ cancels:

$\frac{- 1}{3 \left(3 + h\right)}$

$\frac{- 1}{9 + 3 h}$