If x+1/x=1 , then the value of (x² + 7x + 1)/(x² + 11x + 1)=?

If x+1/x=1 , then the value of (x² + 7x + 1)/(x² + 11x +…

If $x+\frac{1}{x}=1$ , then the value of $\frac{x^2 + 7x + 1}{x^2 + 11x + 1}=?$

Show answer & explanation

Correct answer: B

Explanation

The correct answer is option 2 i.e. $\frac{2}{3}$ .

We know,

x + 1/x = 1 or x² + 1 = x

⇒ $\frac{x^2 + 7x + 1}{x^2 + 11x + 1}$

⇒ (x + 7x)/(x + 11x) = 8x/12x

⇒ 2/3