Incorrect. Rationalize the denominator by multiplying the numerator and denominator by the denominator's conjugate:
$\displaystyle\frac{{{\left(\sqrt{{{3}}}+\sqrt{{{7}}}\right)}}}{{{\left(\sqrt{{{3}}}+\sqrt{{{2}}}\right)}}}\cdot\frac{{{\left(\sqrt{{{3}}}-\sqrt{{{2}}}\right)}}}{{{\left(\sqrt{{{3}}}-\sqrt{{{2}}}\right)}}}\usepackage{cmbright}\Huge\$

Use FOIL and then simplify the radicals.