# Easy one, probably factoring

1. Oct 8, 2007

### tony873004

This is a small step in a larger Calc problem. There's 2 problems in a row where this same arrangement popped up. I have a feeling I'm forgetting something basic. How does $${\frac{{x^2 }}{{x^2 - 1}}}$$ become $$1 + \frac{1}{{x^2 - 1}}$$ ?
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

2. Oct 8, 2007

### Dick

Use polynomial long division to divide the numerator by the denominator. This gives you quotient, 1, and a remainder, 1. Just like 5/4=1+1/4.

Last edited: Oct 8, 2007
3. Oct 8, 2007

### stunner5000pt

add and subtract 1 from the numerator

then we get

$$\frac{x^2}{x^2 -1} = \frac{x^2 - 1 + 1}{x^2 -1} = \frac{x^2-1}{x^2-1} + \frac{1}{x^2 -1} = 1 + \frac{1}{x^2 + 1}$$

4. Oct 8, 2007

### tony873004

2 great answers. I knew it wasn't hard, but I'd have never come up with either of these on my own. Thanks!!