Solving Exponents: Dividing \frac{xa+b}{xa-2b}

[Gregory.gags]

\frac{(x^a+b)^a-b}{(x^a-2b)^a+2b}

I figured since there is one addition and one subtraction of the same amounts in and out of the brackets, they would cancel each other out leaving just \frac{x}{x} which would be 1 (or possibly x?) but I really have absolutely no idea.

also, and this is a long shot, I'm just guessing now that it could be something along the lines of...

\frac{x^a+b(a-b)}{x^a-2b(a+2b)}??

 

[Gregory.gags]

wow, I don't know why the fraction is like that but i hope you get what I'm trying to say :P (the left {} is the numerator and the right {} is the denominator )

 

[Mark44]

\frac{(x^a+b)^a-b}{(x^a-2b)^a+2b}

I figured since there is one addition and one subtraction of the same amounts in and out of the brackets, they would cancel each other out leaving just \frac{x}{x} which would be 1 (or possibly x?) but I really have absolutely no idea.

also, and this is a long shot, I'm just guessing now that it could be something along the lines of...

\frac{x^a+b(a-b)}{x^a-2b(a+2b)}??

This last part is what you want to do, since (x^a)^b = x^ab.
The reason that your LaTeX expressions aren't rendering correctly is that (I believe) you are mixing in HTML stuff (SUP) with the LaTeX stuff. You're also missing some parentheses.

This is what you want.

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