Question

2root3 - root5/2root3+3root3

Answer 1

Heya there !!!
Here is the answer you were looking for:
$\frac{2 \sqrt{3} - \sqrt{5} }{2 \sqrt{3} + 3 \sqrt{3} }$

On rationalizing the denominator we get,

$= \frac{2 \sqrt{3} - \sqrt{5} }{2 \sqrt{3} + 3 \sqrt{3} } \times \frac{2 \sqrt{3} - 3 \sqrt{3} }{2 \sqrt{3} - 3 \sqrt{3} } \\ \\ = \frac{2 \sqrt{3}(2 \sqrt{3} - 3 \sqrt{3}) - \sqrt{5} (2 \sqrt{3} - 3 \sqrt{3}) }{ {(2 \sqrt{3}) }^{2} - {(3 \sqrt{3} )}^{2} } \\ \\ = \frac{12 - 18 - 2 \sqrt{15} - 3 \sqrt{15} }{12 - 18} \\ \\ = \frac{ - 6 - 5 \sqrt{15} }{ - 6} \\ \\ = \frac{6 + 5 \sqrt{15} }{6}$

Hope this helps!!!

If you have any doubt regarding to my answer, please ask in the comment section ^_^

@Mahak24

Thanks...
☺☺

Answer 2

Answer:

Step-by-step explanation:

Heya there !!!

Here is the answer you were looking for:

On rationalizing the denominator we get,

Hope this helps!!!

If you have any doubt regarding to my answer, please ask in the comment section ^_^

@Mahak24

Thanks...

☺☺