You did not distribute when multiplying the numerator by the denominator's conjugate. Multiply the numerator and denominator by the conjugate of the denominator:

$\displaystyle\frac{\sqrt{{a}}}{{{6}-\sqrt{{a}}}}\cdot\frac{{{6}+\sqrt{{a}}}}{{{6}+\sqrt{{a}}}}\usepackage{cmbright}\Huge\$

Distribute on top and use FOIL on the bottom. Simplify radicals.