Quantitative Aptitude Ques 2355

Question: If $ x+\frac{1}{x}=1, $ then the value of $ \frac{x^{2}+3x+1}{x^{2}+7x+1} $ is

Options:

A) $ \frac{1}{2} $

B) $ \frac{3}{7} $

C) 2

D) 1

Show Answer

Answer:

Correct Answer: A

Solution:

  • Given, $ x+\frac{1}{x}=1 $ $ \frac{x^{2}+3x+1}{x^{2}+7x+1}=\frac{x( x+\frac{1}{x} )+3x}{x( x+\frac{1}{x} )+7x}=\frac{x+3x}{x+7x} $ $ =\frac{4x}{8x}=\frac{1}{2}=1:2 $