Question 859400
Simple fraction skills to start with.

What you show is {{{x+1/x=3}}} if you meant what you wrote.
Denominator is x.
{{{x(x/x)+1/x=3}}}
{{{(x^2+1)/x=3}}}
{{{x(x^2+1)/x=3x}}}
{{{x^2+1=3x}}}
{{{x^2-3x+1=0}}}


The quadratic expression is not factorable.  Easiest way to solve is use the general solution for a quadratic equation.

{{{x=(3+- sqrt(9-4))/2}}}
{{{highlight(x=(3+- sqrt(5))/2)}}} and both will work in the original equation.