Rationalising the denominator by Boxed Rockets

Rationalise the Denominator

\frac{4}{6 + \sqrt{5}}

\frac{24 - 4 \sqrt{5}}{31}

\frac{\sqrt{5}}{5 - \sqrt{5}}

\frac{\sqrt{5} + 1}{4}

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

- \frac{1 + 2 \sqrt{7}}{3}

\frac{7 - \sqrt{10}}{3 + \sqrt{10}}

- 31 + -10 \sqrt{10}