It appears that you did not distribute $\displaystyle\sqrt{{{10}}}\usepackage{cmbright}\Huge\$ to both terms in the numerator. The first two steps are:

$\displaystyle\frac{{{9}+\sqrt{{{5}}}}}{\sqrt{{{10}}}}\cdot\frac{\sqrt{{{10}}}}{\sqrt{{{10}}}}=\frac{{{\left({9}+\sqrt{{{5}}}\right)}{\left(\sqrt{{{10}}}\right)}}}{{{\left(\sqrt{{{10}}}\right)}{\left(\sqrt{{{10}}}\right)}}}=\frac{{{9}\sqrt{{{10}}}+\sqrt{{{50}}}}}{\sqrt{{{100}}}}\usepackage{cmbright}\Huge\$

Then simplify radicals. The correct answer is: $\displaystyle\frac{{{9}\sqrt{{{10}}}+{5}\sqrt{{{2}}}}}{{10}}\usepackage{cmbright}\Huge\$