Question

Rationalise the denominator:
√2−√3
---------------
3√2−2√3

Answer 1

Answer:

$\frac{ \sqrt{2} - \sqrt{3} }{3 \sqrt{2} - 2 \sqrt{3} } \\ \\ \\ = \frac{ \sqrt{2} - \sqrt{3} }{3 \sqrt{2} - 2 \sqrt{3} } \times \frac{3 \sqrt{2} + 2 \sqrt{3} }{3 \sqrt{2} + 2 \sqrt{3} } \\ \\ \\ = \frac{3 \sqrt{4} + 2 \sqrt{6} - 3 \sqrt{6} - 2 \sqrt{9} }{ {(3 \sqrt{2} )}^{2} - {(2 \sqrt{3} )}^{2} } \\ \\ \\ = \frac{3 \times 2 - \sqrt{6} - 2 \times 3}{9 \times 2 - 4 \times 3} \\ \\ = \frac{6 - \sqrt{6 } - 6}{18 - 12} \\ \\ = \frac{ - \sqrt{6} }{6}$

• Thnku ;)