\(\displaystyle \L \frac{1}{ 5\, -\, log x}\, +\, \frac{ 2}{ 1\, +\, log x }\, =\, 1\)
\(\displaystyle \L \frac{\(1\,+\,logx\) \,+\, 2\(5\,-l\,og(x)\)}{ (5\,-\,log x)(1\, +\, log x)}\, =\, 1\) (combine)
\(\displaystyle \L \(1\,+\,logx\)\, +\, 2\(5\,-\,log(x)\)\, =\, (5\,-\,log x)(1\, +\, log x)\) (multiply both sides by the denominator)
\(\displaystyle \L 11\, -\, log(x)\, =\, (5\,-\,log x)(1\, +\, log x)\) (simplify)
Now multiply out and move everything to one side and solve the resulting quadratic equation.
