Question

solve this. please I will mark your anwser brainliest ​

Answer 1

Answer:

Step-by-step explanation:

the answer is 0

and the the explanation is attached.

Answer 2

ANSWER:

• THE VALUE OF THE GIVEN EXPRESSION IS 0

GIVEN:

$\frac{1}{2 + \sqrt{3} } + \frac{2}{ \sqrt{5} - \sqrt{3} } + \frac{1}{2 - \sqrt{5} }$

TO FIND:

• Value of above expression

SOLUTION:

$\frac{1}{2 + \sqrt{3} } + \frac{2}{ \sqrt{5} - \sqrt{3} } + \frac{1}{2 - \sqrt{5} }$

We will rationalise the above expression :

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

Now 2nd part

$= \frac{2}{ \sqrt{5} - \sqrt{3} } \\ = \frac{2 \times ( \sqrt{5} + \sqrt{3}) }{( \sqrt{5} - \sqrt{3} )( \sqrt{5} + \sqrt{3} )} \\ = \frac{ \:2 \times ( \sqrt{5} + \sqrt{3} ) \: }{2} \\ = \sqrt{5} + \sqrt{3}$

Now 3rd part

$= \frac{1}{2 - \sqrt{5} } \\ = \frac{1 \times (2 + \sqrt{5} )}{(2 - \sqrt{5} )(2 + \sqrt{5)} } \\ = \frac{2 + \sqrt{5} }{4 - 5} \\ = - 2 - \sqrt{5}$

Now putting all these together

$= 2 - \sqrt{3} + \sqrt{5} + \sqrt{3} - 2 - \sqrt{5} \\ (2 - 2) + ( \sqrt{3} - \sqrt{3} ) + ( - \sqrt{5} - \sqrt{5} ) \\ = 0 + 0 + 0 \\ = 0$

THE VALUE OF THE GIVEN EXPRESSION IS 0.