Question

rationalise the denominator of the following:​

Answer 1

$= \frac{ \sqrt{3} + \sqrt{2} }{2 \sqrt{3} - 3 \sqrt{2} }$

$= \frac{ \sqrt{3} + \sqrt{2} }{2 \sqrt{3} - 3 \sqrt{2} } \times \frac{2 \sqrt{3} + 3 \sqrt{2} }{2 \sqrt{3} + 3 \sqrt{2} }$

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

$= \frac{(2 \times 3) + (3 \times 2}{(4 \times 3) - (9 \times 2)}$

$</p><p> = \frac{12}{12 - 18} \\ </p><p>= \frac{12}{ - 6} \\ = \frac{2}{ - 1}$

Answer 2

Step-by-step explanation:

$\frac{ \sqrt{3} + \sqrt{2} }{2 \sqrt{3} - 3 \sqrt{2} } \\ = \frac{ \sqrt{3} + \sqrt{2} }{2 \sqrt{3} - 3 \sqrt{2} } \times \frac{2 \sqrt{3} + 3 \sqrt{2} }{2 \sqrt{3} + 3 \sqrt{2} } \\ = \frac{6 + 3 \sqrt{6} + 2 \sqrt{6} + 6 }{(2 \sqrt{3}) ^{2} - (3 \sqrt{2} ) ^{2} } \\ = \frac{12 + 5 \sqrt{6} }{12 - 18} \\ = \frac{12 + 5 \sqrt{6} }{ - 6} \\ = \frac{ - 12 - 5 \sqrt{6} }{6}$