Math, asked by narendrakumar7778, 8 months ago

simplify under root 6 divided by under root 2 + under root 3 + 3 / under root 6 + under root 3 minus 4 root 3 divided by under root 6 + under root 2​

Answers

Answered by Dakshfabulous
0

Answer:

Given expression is,

\frac{\sqrt{6} }{\sqrt{2} + \sqrt{3} } + \frac{3\sqrt{2} }{\sqrt{6}+\sqrt{3} } - \frac{4\sqrt{3} }{\sqrt{6}+\sqrt{2} }

2

+

3

6

+

6

+

3

3

2

6

+

2

4

3

By rationalizing each term,

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

(

3

)

2

−(

2

)

2

6

(−

2

+

3

)

+

(

6

)

2

−(

3

)

2

3

2

(

6

3

)

(

6

)

2

−(

2

)

2

4

3

(

6

2

)

=\sqrt{6}(-\sqrt{2} + \sqrt{3})+\sqrt{2}(\sqrt{6}-\sqrt{3} ) -\sqrt{3} (\sqrt{6}-\sqrt{2} )=

6

(−

2

+

3

)+

2

(

6

3

)−

3

(

6

2

)

=-\sqrt{12} + \sqrt{18} + \sqrt{12} - \sqrt{6} - \sqrt{18} + \sqrt{6}=−

12

+

18

+

12

6

18

+

6

=0=0

Hence,

\frac{\sqrt{6} }{\sqrt{2} + \sqrt{3} } + \frac{3\sqrt{2} }{\sqrt{6}+\sqrt{3} } - \frac{4\sqrt{3} }{\sqrt{6}+\sqrt{2} }=0

2

+

3

6

+

6

+

3

3

2

6

+

2

4

3

=0

Answered by kkumari251218
0

Answer:

Is it like this...

(√6/√2) + (√3 +3) /√6 + (√3 - 4√3) /√6 + √2.

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