# Math simplify problem

#### rockytriton

I have a problem where I got the final answer:

Code:
       1              1
-  ---------   -  --------
(u - 1)^2       (u + 1)^2

which is correct, but the book further simplifies it to:

Code:
     2(1 + u^2)
-  -------------
(u^2 - 1)^2
I tried and tried, but couldn't figure out how to simplify it to that result. Can someone please explain the process to me?

Thanks!

#### HallsofIvy

Do you remember adding fractions from fourth grade arithmetic?

Get a common denominator and add.

The denominator of one fraction is (u-1)2= (u-1)(u-1) and the denominator of the other is (u+1)2[/sup= (u+1)(u+1). The "least common denominator" is (u-1)(u-1)(u+1)(u+1)= (u-1)(u+1)(u-1)(u+1)= (u2-1)(u2-1)= (u2-1)2.
$$-\frac{1}{(u-1)^2}- \frac{1}{(u+1)^2}= -\frac{(u+1)^2}{(u-1)^2(u+1)^2}-\frac{(u-1)^2}{(u-1)^2(u+1)^2}$$
$$= -\frac{u^2+ 2u+ 1}{(u^2-1)^2}-\frac{u^2-2u+1}{(u^2-1)^2}$$
$$= -\frac{2u^2+ 2}{(u^2-1)^2}= -\frac{2(u^2+1)}{(u^2-1)^2}$$

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