Rationalising the denominator by Boxed Rockets

Rationalise the Denominator

\frac{4}{2 + \sqrt{7}}

- \frac{8 - 4 \sqrt{7}}{3}

\frac{\sqrt{6}}{10 + \sqrt{6}}

\frac{5 \sqrt{6} - 3}{47}

\frac{2 + \sqrt{5}}{9 + \sqrt{5}}

\frac{13 + 7 \sqrt{5}}{76}

\frac{2 + \sqrt{3}}{10 - \sqrt{3}}

\frac{23 + 12 \sqrt{3}}{97}