You may have thought that the 4 on the top and the bottom would simplify to 1. That kind of simplification would hold only if 4 were a factor of the denominator. Multiply the numerator and denominator by the conjugate of the denominator:

$\displaystyle\frac{{{4}}}{{{\left({4}+\sqrt{{{x}}}\right)}}}\cdot\frac{{{\left({4}-\sqrt{{{x}}}\right)}}}{{{\left({4}-\sqrt{{{x}}}\right)}}}\usepackage{cmbright}\Huge\$

Use the Distributive Property and FOIL and simplify radicals.