Homework Help: Really Simple!

1. Nov 30, 2007

danni7070

How do I simplify this?

$$\frac{1}{x-2} - \frac{1}{x^2-4} = \frac{(x^2-4)-(x-2)}{(x^2-4)(x-2)}$$

2. Nov 30, 2007

Dick

Combine the 4 and 2 in the numerator so you have a single quadratic. Then see if it factors so you can see of if there are any common factors you can cancel.

3. Nov 30, 2007

danni7070

$$\frac{x^2-x-2}{(x^2-4)(x-2)}$$

I know I should be able to see this instantly but I'm not! What comes next?

4. Nov 30, 2007

Dick

You don't have to see it instantly. Can you factor the numerator?

5. Nov 30, 2007

danni7070

Like this?

$$\frac{x^2-x-2}{(x-2)(x+2)(x-2)}$$

Last edited: Nov 30, 2007
6. Nov 30, 2007

danni7070

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

The final step is the answer but I don't know how to get there. What are the rules here?

7. Nov 30, 2007

salman213

after this stage

factor the numerator

x2 - x - 2 = (x-2)(x+1)

right?

then u can cancel t he (x-2) in the numerator and denominator and ur left with that answer that ur looking for

8. Nov 30, 2007

danni7070

I'm having one of those dumb days right know. Jesus!

Thank you Dick and salman213.

9. Nov 30, 2007

HallsofIvy

They said factor the numerator! (Although factoring the denominator doesn't hurt.)