Question

if x+1/x=4 than x/x^2+x+1=?​

Answer 1

Answer:

ans is 3/13 I hope your doubt is resolved now

Answer 2

$\large\text{\underline{Footnote}}$

Given to evaluate;

$\implies\dfrac{x}{x^{2}+x+1}=\dfrac{1}{x+1+\dfrac{1}{x}}$

$\large\text{\underline{Solution}}$

Given condition;

$\implies x+\dfrac{1}{x}=4$

$\implies x+1+\dfrac{1}{x}=5$

Thus,

$\implies \dfrac{1}{x+1+\dfrac{1}{x}}=\dfrac{1}{5}$

$\implies \dfrac{x}{x^{2}+x+1}=\dfrac{1}{5}$

$\large\text{\underline{Conclusion}}$

Hence, the value is equal to $\dfrac{1}{5}$.