ABC26GN0967 · Simplification
Subject: General Aptitude · Chapter: Simplification · Exam: 2006 · Marks: · Difficulty:
If $\frac{x}{y}=\frac{1}{3}$, then $\frac{x^{2}+y^{2}}{x^{2}-y^{2}}=$ ?
(a)$-\frac{10}{9}$
(b)$\frac{5}{4}$
(c)$-\frac{5}{4}$
(d)$-\frac{5}{3}$
Answer
Explanation
$$\begin{aligned} \frac{x^{2}+y^{2}}{x^{2}-y^{2}} & =\frac{\frac{x^{2}}{y^{2}}+1}{\frac{x^{2}}{y^{2}}-1}=\frac{\left(\frac{x}{y}\right)^{2}+1}{\left(\frac{x}{y}\right)^{2}-1}=\frac{\left(\frac{1}{3}\right)^{2}+1}{\left(\frac{1}{3}\right)^{2}-1} \\ & =\frac{\left(\frac{1}{9}+1\right)}{\left(\frac{1}{9}-1\right)}=\frac{10}{9} \times\left(-\frac{9}{8}\right)=-\frac{5}{4} . \end{aligned}$$
Explanation as extracted from the printed page; notation may be imperfect.
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