- Using Rational ExpressionsChoice E
$$ \frac{x}{x+y}+\frac{y}{x-y}=? $$
$$ =\frac{x(x-y)+y(x+y)}{(x+y)(x-y)} $$
$$ =\frac{x^2-xy+xy+y^2}{x^2-y^2} $$
$$ =\frac{x^2+y^2}{x^2-y^2} $$
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$$ \frac{x}{x+y}+\frac{y}{x-y}=? $$
$$ =\frac{x(x-y)+y(x+y)}{(x+y)(x-y)} $$
$$ =\frac{x^2-xy+xy+y^2}{x^2-y^2} $$
$$ =\frac{x^2+y^2}{x^2-y^2} $$
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