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If \( \Large x + \frac{a}{x} = 1 \), then the value of \( \Large \frac{x^{2}+x+a}{x^{3}-x^{2}} \) is

A) -2
B) \( \Large - \frac{a}{2} \)
C) \( \Large \frac{2}{a} \)
D) \( \Large - \frac{2}{a} \)

Correct Answer:




D) \( \Large - \frac{2}{a} \)

Description for Correct answer:

Given, \( \Large x + \frac{a}{x} = 1 \)

=> \( \Large x^{2} + a = x \) ...(i)

=> \( \Large x^{2} - x = -a \) ...(ii)

Now, \( \Large \frac{x^{2} + x + a}{x^{3} - x^{2}} = \frac{x + x}{x \left(x^{2} - x\right) } \) [from Eq. (i)]

= \( \Large \frac{2x}{x \left(-a\right) } \) [from Eq. (ii)]

= \( \Large \frac{2}{-a} \)

Part of solved Simplification questions and answers : >> Elementary Mathematics >> Simplification

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