1. ## Difficult fraction problem

I don't know how this can be simplified or solved, tried synthetic division.. no good.
Help appreciated

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

2. ## Re: Difficult fraction problem

I don't know if you would consider this simpler, but

\displaystyle \displaystyle \begin{align*} \frac{x^4 + (2xy^2)^2 - 3y}{(xy)^2} &= \frac{x^4 + 2x^2y^4 - 3y}{x^2y^2} \\ &= \frac{x^4}{x^2y^2} + \frac{2xy^2}{x^2y^2} - \frac{3y}{x^2y^2} \\ &= \frac{x^2}{y^2} + \frac{2}{x} - \frac{3}{x^2y} \end{align*}

3. ## Re: Difficult fraction problem

I've done that, but it seems incomplete.
I feel like I'm missing something.

4. ## Re: Difficult fraction problem

Originally Posted by Prove It
I don't know if you would consider this simpler, but

\displaystyle \displaystyle \begin{align*} \frac{x^4 + (2xy^2)^2 - 3y}{(xy)^2} &= \frac{x^4 + 2x^2y^4 - 3y}{x^2y^2} \\ &= \frac{x^4}{x^2y^2} + \frac{2xy^2}{x^2y^2} - \frac{3y}{x^2y^2} \\ &= \frac{x^2}{y^2} + \frac{2}{x} - \frac{3}{x^2y} \end{align*}
No, $\displaystyle (2xy^2)^2= 4x^2y^4$ so that should be
$\displaystyle \frac{x^4 + (2xy^2)^2 - 3y}{(xy)^2} &= \frac{x^4 + 4x^2y^4 - 3y}{x^2y^2}$
and the final result should be
$\displaystyle \frac{x^2}{y^2} + \frac{4}{x} - \frac{3}{x^2y}$