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

Solution:
Given,

$= \dfrac{2√3 - 3√2}{2√3 + 3√2}$

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

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

$= \dfrac{(2√3)² - 2×2√3×3√2 + (3√2)²}{4×3 - 9×2}$

$= \dfrac{4×3 - 12√6 + 9×2}{12 - 18}$

$= \dfrac{12 -12√6 +18}{-6}$

$= \dfrac{30 - 12√6}{-6}$

$= \dfrac{6(5 -2√6)}{-6}$

$= -(5-2√6)$

$= 2√6 - 5$
= Answer