Question

Rationalise the denominator and simplify:

$\frac{2\sqrt{6}-\sqrt{5}}{3\sqrt{5}-2\sqrt{6}}$

Answer 1

Given: $\frac{2\sqrt{6}-\sqrt{5}}{3\sqrt{5}-2\sqrt{6}}$

Multiplying both numerator and denominator by $3\sqrt{5}+2\sqrt{6}$ to rationalise the denominator.

$=\frac{(2\sqrt{6}-\sqrt{5})(3\sqrt{5}+2\sqrt{6})}{(3\sqrt{5}-2\sqrt{6})(3\sqrt{5}+2\sqrt{6})}$

$=\frac{6\sqrt{30}+24-15-2\sqrt{30}}{(3\sqrt{5}{)}^2-(2\sqrt{6}{)}^2}$

$=\frac{4\sqrt{30}+9}{45-24}$

$=\frac{4\sqrt{30}+9}{21}$