# 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

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