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Simplify $\dfrac{x}{x+y}+\dfrac{x^{2}}{y^{2} - x^{2}}$
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factorize denominators to get LCD

$= \frac{x}{(x+y)} + \frac{x^2}{(y-x)(y+x)}$

$= \frac{[x(y-x)+x]}{(y-x)(y+x)}$

$= \frac{(xy-x^2 + x^2)}{(y-x)(y+x)}$

$= \frac{xy}{(y-x)(y+x)}$
by Diamond (44,734 points)

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