1. Simplifying a rational function

((x^-7)(y^2)) / ((x^-3) + y^-4))

and I'm trying to simplify it.

So I've gotten down to this:

((x^3)(y^6)) / ((y^4)(x^7)) + x^10)

and I guess this could technically be an acceptable answer but when I punched this into my calculator, I got it simplified to:

(y^6) / ((x^4)(y^4) + x^7)

Can someone show me (with steps please) how to get that final result.

Thank-you!

2. can you confirm this is the expression?

$\displaystyle \frac{x^{-7}y^2}{x^{-3}+y^{-4}}$

If so

$\displaystyle \frac{y^2}{x^7(x^{-3}+y^{-4})}$

expanding the denominator

$\displaystyle \frac{y^2}{(x^{4}+x^7y^{-4})}$

It can't get much simplier than this.

3. Yup that was the original function.

Cool thank-you. That makes solving it a lot simpler actually. I was doing things the long way.

4. $\displaystyle \frac{y^2}{x^7\left ( \frac{1}{x^3}+\frac{1}{y^4} \right )}=\frac{y^2}{x^7x^-3+x^7y^-4}=\frac{y^2}{x^4+x^7y^-4}$ multiply the denominator and the nominator by $\displaystyle y^4$