The expression ((x+1/y)a · (x-1/y)b)/((y+1/x)a · (y-1/x)b) reduces to · ABC26GN1974

Subject: General Aptitude · Chapter: Surds and Indices

The expression $\frac{\left(x+\frac{1}{y}\right)^{a} \cdot\left(x-\frac{1}{y}\right)^{b}}{\left(y+\frac{1}{x}\right)^{a} \cdot\left(y-\frac{1}{x}\right)^{b}}$ reduces to
(a)$\left(\frac{x}{y}\right)^{a-b}$
(b)$\left(\frac{y}{x}\right)^{a-b}$
(c)$\left(\frac{x}{y}\right)^{a+b}$
(d)$\left(\frac{y}{x}\right)^{a+b}$
Answer
Answer (as printed): C
Explanation
Given Exp. $=\frac{\left(\frac{x y+1}{y}\right)^{a} \cdot\left(\frac{x y-1}{y}\right)^{b}}{\left(\frac{x y+1}{x}\right)^{a} \cdot\left(\frac{x y-1}{x}\right)^{b}}$ $$\begin{aligned} & =\frac{(x y+1)^{a} \cdot(x y-1)^{b} \cdot x^{a} \cdot x^{b}}{(x y+1)^{a} \cdot(x y-1)^{b} \cdot y^{a} \cdot y^{b}} \\ & =\frac{x^{a+b}}{y^{a+b}}=\left(\frac{x}{y}\right)^{a+b} . \end{aligned}$$

Explanation as extracted from the printed page; notation may be imperfect.

Study loop for Surds and Indices

1. Practise the PYQsPrevious-year questions, with answers

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