Quantitative Aptitude Ques 1072

Question: If $ x+\frac{1}{x}=3, $ then the value of $ \frac{3x^{2}-4x+3}{x^{2}-x+1} $ is

Options:

A) $ \frac{4}{3} $

B) $ \frac{3}{2} $

C) $ \frac{5}{2} $

D) $ \frac{5}{3} $

Show Answer

Answer:

Correct Answer: C

Solution:

  • [c] Given, $ ( x+\frac{1}{x} )=3, $ Given function $ =\frac{3x^{2}-4x+3}{x^{2}-x+1}=\frac{x( 3x-4+\frac{3}{x} )}{x( x-1+\frac{1}{x} )} $ $ =\frac{3x+\frac{3}{x}-4}{x+\frac{1}{x}-1}=\frac{3( x+\frac{1}{x} )-4}{( x+\frac{1}{x} )-1} $ $ =\frac{3\times 3-4}{3-1}=\frac{9-4}{2}=\frac{5}{2} $
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