# Simplifying an expression

• Sep 18th 2009, 04:28 PM
frozenflames
Simplifying an expression
the one that is still confusing me is the simplification of:

Imageshack - 07e3be3572344e492265b64
• Sep 18th 2009, 04:36 PM
redsoxfan325
Quote:

Originally Posted by frozenflames
thanks a lot, but i figured that one out.

the one that is still confusing me is the simplification of:

Imageshack - 07e3be3572344e492265b64

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

Start by finding common denominators for the two fractions in the numerator and combining them into one fraction:

$\frac{\frac{2}{a+h}-\frac{2}{a}}{h}=\frac{\frac{2a}{a(a+h)}-\frac{2(a+h)}{a(a+h)}}{h}$ $=\frac{\frac{2a-2(a+h)}{a(a+h)}}{h}=\frac{\frac{2a-2a+2h}{a(a+h)}}{h}=\frac{\frac{2h}{a(a+h)}}{h}$

To divide fractions, multiply the top fraction by the reciprocal of the bottom one:

$\frac{\frac{2h}{a(a+h)}}{h}=\frac{2h}{a(a+h)}\cdot \frac{1}{h}=\frac{2h}{ah(a+h)}$

Cancel the $h$'s and you're done:

$\frac{2h}{ah(a+h)}=\boxed{\frac{2}{a(a+h)}}$