Simplifying rational functions with common factors

[3.141592654]

Homework Statement

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

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

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

Homework 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.

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.

 

[3.141592654]

Nevermind, I figured out all the answers!

 

[HallsofIvy]

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

 

[3.141592654]

Indeed I did.

 

[HallsofIvy]

Excellent!