ABC26GN1198 · Simplification
Subject: General Aptitude · Chapter: Simplification · Exam: 2009 · Marks: · Difficulty:
$\frac{(a-b)^{2}-(a+b)^{2}}{-4 a}=\frac{x}{y}$. On simplifying the given equation, which of the following equations will be obtained?
(a)$x y=b$
(b)$b x=y$
(c)$a b=x$
(d)$y b=x$
Answer
Explanation
$\frac{(a-b)^{2}-(a+b)^{2}}{-4 a}=\frac{x}{y} \Leftrightarrow \frac{\left(a^{2}+b^{2}-2 a b\right)-\left(a^{2}+b^{2}+2 a b\right)}{-4 a}$ $$\begin{aligned} & =\frac{x}{y} \\ & \Leftrightarrow \frac{-4 a b}{-4 a}=\frac{x}{y} \Leftrightarrow b=\frac{x}{y} \Leftrightarrow x=y b . \end{aligned}$$
Explanation as extracted from the printed page; notation may be imperfect.
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