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If \( \Large \frac{a}{b}-\frac{b}{a}=\frac{x}{y} \) and \( \Large \frac{a}{b}+\frac{b}{a}= x - y \) , then what is the value of x?


A) \( \Large \frac{a+b}{a} \)

B) \( \Large \frac{a+b}{b} \)

C) \( \Large \frac{a-b}{a} \)

D) None of these

Correct Answer:
D) None of these

Description for Correct answer:

Given equations are

\( \Large \frac{a}{b}-\frac{b}{a}=\frac{x}{y} \)

= \( \Large y = \frac{x}{ \left(\frac{a}{b}-\frac{b}{a}\right) } \) ...(i)

and \( \Large \frac{a}{b}+\frac{b}{a}=x-y \) ...(ii)

From Eqs. (i) and (ii),

\( \Large \frac{a}{b}+\frac{b}{a}=x-\frac{x}{ \left(\frac{a}{b}-\frac{b}{a}\right) } \)

= \( \Large \left(\frac{a}{b}+\frac{b}{a}\right) \left(\frac{a}{b}-\frac{b}{a}\right) = x \left(\frac{a}{b}-\frac{b}{a}-1\right) \)

= \( \Large \left(\frac{a^{2}}{b^{2}}-\frac{b^{2}}{a^{2}}\right) \)

= \( \Large x \left(\frac{a^{2}-b^{2}-ab}{ab}\right) \)

= \( \Large x=\frac{ab}{ \left(a^{2}-b^{2}-ab\right) } \times \left(\frac{a^{4}-b^{4}}{a^{2}b^{2}}\right) \)

= \( \Large x=\frac{ \left(a^{4}-b^{4}\right) }{a^{2}-b^{2}-ab} \times \frac{1}{ab} \)

= \( \Large \frac{ \left(a-b\right) \left(a+b\right) \left(a^{2}+b^{2}\right) }{ab \left(a^{2}-b^{2}-ab\right) } \)


Part of solved Linear Equations questions and answers : >> Aptitude >> Linear Equations




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