Stuck on a Textbook Problem? Get a Hint Here!

[Swatch]

I have a textbook problem I am trying to solve with no luck.
I know 1/(u^2 -1) = 1/2 [ 1/(u-1) - 1/(u+1) ]
I come so far to see that 1/(u^2 -1) = 1/ [(u-1)(u+1) ]
But I don't know what comes next. Could somebody please give me a hint.

 

[Physics Monkey]

Hint: This is called partial fraction decomposition, and you can think of it as the opposite of finding a common denominator.

 

[TD]

Well you factored your denominator correctly. Now try to work the other way arround. "Suppose" you can split your fraction into two parts, and then try to find the right coefficients. So suppose that:

$$\frac{1}{{u^2 - 1}} = \frac{A}{{u - 1}} + \frac{B}{{u + 1}}$$

Now try to find A and B.

 

[Swatch]

Thanks, it worked.