SOLUTION: {{{( ( (a+b)^2-9)/((a-b)^2-9))) * ((a-b-3)/(a+b+3))}}}

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: {{{( ( (a+b)^2-9)/((a-b)^2-9))) * ((a-b-3)/(a+b+3))}}}      Log On


   

Question 36045:
Answer by rapaljer(4671) About Me  (Show Source):
You can put this solution on YOUR website!
WOW!! Somebody who can write an equation box!! Congratulations for that.

Start by factoring the numerator and denominator of the first fraction as the difference of two squares.

To lead into this, start with
x%5E2+-+9=+%28x-3%29%2A%28x%2B3%29, which is pretty obvious.
In the same way, the slightly more complicated difference of squares +%28a%2Bb%29%5E2+-+9+ as
+%28a%2Bb%29%5E2+-+9+=+%28%28a%2Bb%29-3%29%2A%28%28a%2Bb%29%2B3%29+ and
+%28a-b%29%5E2+-+9+=+%28%28a-b%29-3%29%2A%28%28a-b%29%2B3%29+.

So, factor the first fraction, and it should look like this, giving you some factors that will divide out:

* %28%28a-b-3%29%2F%28a%2Bb%2B3%29%29

Now, both factors in the second fraction match up and divide out with one of the factors in the first fraction. Divide out the %28a-b-3%29 and the +%28a%2Bb%2B3%29 , which leaves:
+%28a%2Bb-3%29%2F%28a-b%2B3%29+

R^2 at SCC