# Simplifying rational functions with common factors

1. Jul 24, 2009

### 3.141592654

1. The problem statement, all variables and given/known data

Simply these rational functions: [$$\sqrt{(X^2)+12}$$-4]/(X-2)

(2-$$\sqrt{(X^2)-5}$$)/(X+3)

(X-1)/($$\sqrt{X+3}$$-2)

2. Relevant equations

The only example in the book used the technique of multiplying the numerator and denominator by the function p(x) if p(x) is the function in the above equations with a square root in it, except they switched the sign.

3. The attempt at a solution

For example, for the equation [$$\sqrt{(X^2)+12}$$-4]/(X-2) you would multiply both sides by [$$\sqrt{(X^2)+12}$$+4], but this yields ([(x^2)+12]-16)/(X-2)($$\sqrt{(X^2)-12}$$+4), which I'm not sure simplifies. Could you please explain how to solve these problems? Thank you.

2. Jul 25, 2009

### 3.141592654

Nevermind, I figured out all the answers!

3. Jul 25, 2009

### HallsofIvy

Staff Emeritus
Did you figure out that those aren't rational functions?

4. Jul 25, 2009

### 3.141592654

Indeed I did.

5. Jul 25, 2009

### HallsofIvy

Staff Emeritus
Excellent!