Question 1036158
.
x+1/x=5, find the value of x/x^2+x+1
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~


<pre>
Instead of {{{x/(x^2 + x + 1)}}}, let us consider its reciprocal {{{(x^2 + x + 1)/x}}}.


It is equal to {{{x + 1 + 1/x}}}    (1).


Since {{{x + 1/x}}} = 5  (given !), we have for (1) {{{x + 1 + 1/x}}} = 5 + 1 = 6.


Therefore,  {{{x/(x^2 + x + 1)}}} = {{{1/6}}}.
</pre>