Rewrite the first factor as a single fraction. Do this by rewriting $1$ as $\frac{y}{y}$.

$\large \left(\frac{y+x}{y}\right)\left(\frac{4y^2}{x^2-y^2}\right)$

Since you are dividing, invert the second fraction and multiply.
Be sure to factor all of the expressions and then simplify.

$\large \left(\frac{x+x^{-3}}{x^{-2}+x^{-1}}\right)^1$

$\large \frac{x+\frac{1}{x^3}}{\frac{1}{x^2}+\frac{1}{x}}$

$\large \left(\frac{x+\frac{1}{x^3}}{\frac{1}{x^2}+\frac{1}{x}}\right)\left(\frac{\frac{x^3}{1}}{\frac{x^3}{1}}\right)$