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If \( \Large x + \frac{1}{x} = 2 \), then \( \Large \frac{2x^{2} + 2}{3x^{2} + 5x + 3} \) = ?

A) \( \Large \frac{4}{11} \)
B) \( \Large \frac{1}{2} \)
C) \( \Large 1\frac{3}{4} \)
D) \( \Large 2\frac{1}{3} \)

Correct Answer:

A) \( \Large \frac{4}{11} \)

Description for Correct answer:

Given expression = \( \Large \frac{2x^{2}+2}{3x^{2}+3+5x} \)

On dividing numerator and denominator by x, we get

\( \Large \frac{2 \left(x+\frac{1}{x}\right) }{3 \left(x+\frac{1}{x}\right)+5 } = \frac{2 \times 2}{3 \times 2 + 5} = \frac{4}{11} \) [given \( \Large x + \frac{1}{x} \) =2]

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

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