Question 478468
{{{x/(x+1) + (x+1)/x = 13/6}}}

==> {{{(x^2 + x^2 + 2x + 1)/(x(x+1)) = 13/6}}}

==> {{{12x^2 + 12x + 6 = 13x^2 + 13x}}}

==> {{{0 = x^2 + x - 6}}}

==> 0 = (x +3)(x - 2) ==> x = -3,2.

Both satisfy the original equation.  These are the final answers.