If a=x/(x+y) and b=y/(x-y), then a b/(a+b) is equal to · ABC26GN0973
Subject: General Aptitude · Chapter: Simplification
If $a=\frac{x}{x+y}$ and $b=\frac{y}{x-y}$, then $\frac{a b}{a+b}$ is equal to
(a)$\frac{x y}{x^{2}+y^{2}}$
(b)$\frac{x^{2}+y^{2}}{x y}$
(c)$\frac{x}{x+y}$
(d)$\left(\frac{y}{x+y}\right)^{2}$
Answer
Explanation
$\frac{a b}{a+b}=\frac{\frac{x}{x+y} \cdot \frac{y}{x-y}}{\frac{x}{x+y}+\frac{y}{x-y}}=\frac{\frac{x y}{x^{2}-y^{2}}}{\frac{x(x-y)+y(x+y)}{x^{2}-y^{2}}}=\frac{x y}{x^{2}+y^{2}}$.
Explanation as extracted from the printed page; notation may be imperfect.
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