Question

√6/√2+√3 +3×√2/√6+√3 -4×√3/√6+√2

Answer 1

Hey friend,
Here is the answer you were looking for:

Identitiy used :

$(x + y)(x - y) = {x}^{2} - {y}^{2}$

So,
$\frac{ \sqrt{6} }{ \sqrt{2} + \sqrt{3} } + \frac{3 \sqrt{2} }{ \sqrt{6} + \sqrt{3} } - \frac{4 \sqrt{3} }{ \sqrt{6} + \sqrt{2} }$

On rationalizing the denominator we get,

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

On splitting some numbers we get :

$= \frac{ \sqrt{2 \times 2 \times 3} - \sqrt{3 \times 3 \times 2} }{ - 1 } + \frac{3 \sqrt{2 \times 2 \times 3} - 3 \sqrt{6} }{3} - \frac{4 \sqrt{3 \times 3 \times 2} - 4 \sqrt{6} }{4} \\ \\ = - (2 \sqrt{3} - 3 \sqrt{2} ) + \frac{3 \times 2 \sqrt{3} - 3 \sqrt{6} }{3} - \frac{4 \times 3 \sqrt{2} - 4 \sqrt{6} }{4} \\ \\ = - 2 \sqrt{3} + 3 \sqrt{2} + 2 \sqrt{3} - \sqrt{6} - 3 \sqrt{2} + \sqrt{6} \\ \\ = 0$

Hope this helps!!

If you have any doubt regarding to my answer, feel free to ask in the comment section or inbox me if needed.

@Mahak24

Thanks...
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Answer 2

Answer:

Step-by-step explanation:

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