CPM Homework Help : PCT Problem 9-115

Simplify: $\frac { \frac { 1 } { 5 x + h } - \frac { 1 } { 5 x } } { h }$

Hint:

Multiply the numerator and the denominator by $\frac{(5x)(5x+h)}{(5x)(5x+h)}$

Step 1:

$\left( \frac{\frac{1}{5x+h}-\frac{1}{5x}}{h}\right) \left( \frac{(5x)(5x +h)}{(5x)(5x+h)}\right)$

Step 2:

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

Step 3:

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

Step 4:

$\left( \frac{-1}{(5x)(5x+h)}\right)$