I am really having trouble simplifying this equation. The equation is:

(x)(y^-2)(z)/(x)(z)+(x)(y-3)=....? Sorry if it's not clear how I wrote it, hard to do on a computer without the proper symbol, but it basically reads x times y (to the power of negative 2) times z OVER(DIVIDED BY) x times z PLUS x times y (to the power of negative 3).

Now, I'm pretty sure I cannot cancel out all x's, perhaps I can subtract the y exponents from each other? I really have no idea where to start, any help is much appreciated. Tell me if you need clarification of what the problem really is and I'll try my best to explain it.

2. You mean this?
$\displaystyle \dfrac{xy^{-2}z}{xz + xy^{-3}}$ (choice #1)

or this?
$\displaystyle \dfrac{xy^{-2}z}{xz} + xy^{-3}$ (choice #2)
(BTW, learn LaTeX, and you too can type math symbols/expressions/equations )

I'm going to assume you meant choice #1. Start by factoring out an x in the denominator:
$\displaystyle \dfrac{xy^{-2}z}{x(z + y^{-3})}$

Cancel the x's:
$\displaystyle \dfrac{y^{-2}z}{z + y^{-3}}$

Multiply by y^3/y^3:
$\displaystyle \dfrac{y^{-2}z}{z + y^{-3}} \cdot \dfrac{y^3}{y^3}$

$\displaystyle \dfrac{yz}{y^3 z + 1}$

I don't think you can simplify further (correct me if I am wrong).

If you meant choice #2, I'll let someone else work it out.

3. That's exactly it thanks, it was choice one, and you wrote it down perfectly, I should learn Latex as you suggested. Anyways, I followed you up until the last step. You have to multiply top and bottom by y^3? When exponents are being divided (on top of each other) can you not just subtract? So y^-2 minus y^-3, which would give you y^1, in other words just y. Maybe I'm wrong, your answer seems correct, just wondering about the last step. Again, thanks for the help, great step-by-step directions.

4. I think you're asking why I didn't "subtract" the exponents for y from here:
$\displaystyle \dfrac{y^{-2}z}{z + y^{-3}}$
to here:
$\displaystyle \dfrac{yz}{z}$ instead.
The reason is that you can't. The $\displaystyle y^{-3}$ is ADDED to another term in the denominator. If it was MULTIPLIED by another term or expression, like this:
$\displaystyle \dfrac{y^{-2}z}{zy^{-3}}$
then yes, I could "subtract" the exponents for y (and cancel the z's while I'm at it).

5. Ah alright, that makes sense. Thanks for the help.