the one that is still confusing me is the simplification of:
Imageshack - 07e3be3572344e492265b64
the one that is still confusing me is the simplification of:
Imageshack - 07e3be3572344e492265b64
$\displaystyle \frac{\frac{2}{a+h}-\frac{2}{a}}{h}$
Start by finding common denominators for the two fractions in the numerator and combining them into one fraction:
$\displaystyle \frac{\frac{2}{a+h}-\frac{2}{a}}{h}=\frac{\frac{2a}{a(a+h)}-\frac{2(a+h)}{a(a+h)}}{h}$ $\displaystyle =\frac{\frac{2a-2(a+h)}{a(a+h)}}{h}=\frac{\frac{2a-2a+2h}{a(a+h)}}{h}=\frac{\frac{2h}{a(a+h)}}{h}$
To divide fractions, multiply the top fraction by the reciprocal of the bottom one:
$\displaystyle \frac{\frac{2h}{a(a+h)}}{h}=\frac{2h}{a(a+h)}\cdot \frac{1}{h}=\frac{2h}{ah(a+h)}$
Cancel the $\displaystyle h$'s and you're done:
$\displaystyle \frac{2h}{ah(a+h)}=\boxed{\frac{2}{a(a+h)}}$