Question

rationalize the denominator of $5\sqrt{3} - 4\sqrt{2} / 4\sqrt{3} + 3\sqrt{2}$

Answer 1

$\frac{5 \sqrt{3} - 4 \sqrt{2} }{4 \sqrt{3} + 3 \sqrt{2} } \\ \\ = \frac{5 \sqrt{3} - 4 \sqrt{2} }{4 \sqrt{3} + 3 \sqrt{2} } \times \frac{4 \sqrt{3} - 3 \sqrt{2} }{4 \sqrt{3} - 3 \sqrt{2} } \\ \\ = \frac{60 - 15 \sqrt{6} - 16 \sqrt{6} + 24}{48 - 18} \\ \\ = \frac{84 - 31 \sqrt{6} }{30}$