Question

If $\frac{x}{x^2+x+1}=\frac{1}{4}$ then find the value of $x+\frac{1}{x}$.

Answer 1

Given,

$\frac{x}{x^2+x+1}=\frac{1}{4}$

or, $\frac{x^2+x+1}{x}=4$

or, $x+1+\frac{1}{x}=4$

or, $x+\frac{1}{x}=3$.