Banking Quantitative Aptitude Sample Paper Quantitative Aptitude Sample Paper-2

If \[x+\frac{1}{x}=3,\] then the value of \[\frac{3{{x}^{2}}-4x+3}{{{x}^{2}}-x+1}\] is [SSC (10+2) 2014]

A) \[\frac{4}{3}\]

B) \[\frac{3}{2}\]

C) \[\frac{5}{2}\]

D) \[\frac{5}{3}\]

Correct Answer: C

Solution :

[c] Given, \[\left( x+\frac{1}{x} \right)=3,\]

Given function \[=\,\,\frac{3{{x}^{2}}-4x+3}{{{x}^{2}}-x+1}=\frac{x\left( 3x-4+\frac{3}{x} \right)}{x\left( x-1+\frac{1}{x} \right)}\]

\[=\,\,\frac{3x+\frac{3}{x}-4}{x+\frac{1}{x}-1}=\,\,\frac{3\left( x+\frac{1}{x} \right)-4}{\left( x+\frac{1}{x} \right)-1}\]

\[=\frac{3\times 3-4}{3-1}=\frac{9-4}{2}=\frac{5}{2}\]