$$\frac{x-2y}{4y^{2}-x^{2}}$$
$-\frac{1}{x+2y}$
$$\frac{x-2y}{\left(x+2y\right)\left(-x+2y\right)}$$
$$\frac{-\left(-x+2y\right)}{\left(x+2y\right)\left(-x+2y\right)}$$
$$\frac{-1}{x+2y}$$
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$-\frac{2}{2x+4y}$
