Question: Rationalize the denominators and simplify: $\dfrac{5√3}{2√3 - √2}$

Solution:
Given,

$= \dfrac{5√3}{2√3 - √2}$

$= \dfrac{5√3}{2√3 - √2} × \dfrac{2√3 + √2}{2√3 + √2}$

$= \dfrac{5√3 (2√3 +√2)}{(2√3)^2 - (√2)^2}$

$= \dfrac{5×2×\sqrt{3×3} + 5×\sqrt{2×3})}{12 - 2}$

$= \dfrac{10×3 + 5√6}{10}$

$= \dfrac{30 + 5√6}{10}$

$= \dfrac{5(6 + √6)}{10}$

$= \dfrac{1}{2} (6+√6)$
= Answer