Question

I need a hand written answer.
plz explain it step by step.
​

Answer 1

Answer:this answer is0 because many reason

Step-by-step explanation:

There are 200 type to make

Answer 2

0

Step-by-step explanation:

To Solve:

$\dfrac{ \sqrt{6} }{ \sqrt{2} + \sqrt{3}} + \dfrac{3 \sqrt{2} }{ \sqrt{6} + \sqrt{3}} - \dfrac{4 \sqrt{3} }{ \sqrt{6} + \sqrt{2} }$

Solution:

1) Rationalize in split way or combine way.

I will solve it is split way.

2) Right the Rationalize terms and as follow the question.

1st term

$\frac{ \sqrt{6} }{ \sqrt{2} + \sqrt{3}} \\ \\ = \frac{ \sqrt{6}( \sqrt{2} - \sqrt{3})}{( \sqrt{2} + \sqrt{3})( \sqrt{2} - \sqrt{3})} \\ \\ = \frac{ \sqrt{6}. \sqrt{2} - \sqrt{6}. \sqrt{3} }{ {( \sqrt{2})}^{2} - {( \sqrt{3})}^{2} } \: \: \because (x + y)(x - y) = {x}^{2} - {y}^{2} \\ \\ = \frac{ \sqrt{12}- \sqrt{18} }{2 - 3} \\ \\ = \frac{2 \sqrt{3} - 3 \sqrt{2} }{ - 1} \\ \\ = - 2 \sqrt{3} + 3 \sqrt{2}$

2nd term

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

3rd term

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

Now, In question...

$\dfrac{ \sqrt{6} }{ \sqrt{2} + \sqrt{3}} + \dfrac{3 \sqrt{2} }{ \sqrt{6} + \sqrt{3}} - \dfrac{4 \sqrt{3} }{ \sqrt{6} + \sqrt{2} } \\ \\ = ( - 2 \sqrt{3} + 3 \sqrt{2}) +( 2 \sqrt{3} - \sqrt{6}) - (3 \sqrt{2} - \sqrt{6} ) \\ \\ = - 2 \sqrt{3} + 3 \sqrt{2} + 2 \sqrt{3} - \sqrt{6} - 3 \sqrt{2} + \sqrt{6} \\ \\ = - \cancel{2 \sqrt{3}} + \cancel{3 \sqrt{2}} +\cancel{2 \sqrt{3}} - \cancel{\sqrt{6}} -\cancel{ 3 \sqrt{2}} + \cancel{\sqrt{6}} \\ \\ = 0$

Therefore, the required answer is 0.