Rationalise the denominator of the following number:
$\frac{1}{5+2 \sqrt{3}}$

(A) To rationalise the denominator,multiply the numerator and the denominator by the conjugate of the denominator,which is $(5-2 \sqrt{3})$.
$\frac{1}{5+2 \sqrt{3}} = \frac{1}{5+2 \sqrt{3}} \times \frac{5-2 \sqrt{3}}{5-2 \sqrt{3}}$
Using the identity $(a+b)(a-b) = a^2 - b^2$ in the denominator:
$= \frac{5-2 \sqrt{3}}{(5)^2 - (2 \sqrt{3})^2}$
$= \frac{5-2 \sqrt{3}}{25 - (4 \times 3)}$
$= \frac{5-2 \sqrt{3}}{25 - 12}$
$= \frac{5-2 \sqrt{3}}{13}$