# Help with reducing fraction please!

• March 29th 2009, 12:34 PM
mathchallenged
Hi! Okay, I have this fraction. The instructions specifically say "simplify for all values of a for which the expression is defined", which I'm guessing is a fancy way of asking you to reduce it:
$\frac{1-\frac{2}{a}}{\frac{4}{a^2}-1}$

I multiplied top and bottom by $a^2$ and got this:

$\frac{a^2-2a}{4 - a^2}$

I'm really stuck now. Any help is very much appreciated! Thank you!
• March 29th 2009, 12:55 PM
red_dog
$\frac{a^2-2a}{4-a^2}=\frac{a(a-2)}{(2-a)(2+a)}=-\frac{a}{a+2}$
• March 29th 2009, 01:03 PM
mathchallenged
...Oh man, thanks so much! It seems really obvious now. Ugh, I had the most ridiculously complex attempts scribbled all over my paper. Thanks again!