Question

Please tell the answer of this question​

Answer 1

Given :

•Simplify:

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

To Find:

• The values from this expression =?

Formula :

It is easy to simplify by using rationalizing method :

$\\ \bullet \tt \: \frac{numerator}{denominator} \times \frac{denominator}{denominator}$

Solution :

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

By rationalizing :

$\\ \\ \implies \sf \: \frac{2( \sqrt{5} - \sqrt{3} ) }{( \sqrt{5} + \sqrt{3})( \sqrt{5} - \sqrt{3} )} + \frac{1( \sqrt{3} - \sqrt{2} )}{( \sqrt{3} + \sqrt{2})( \sqrt{3} - \sqrt{2} ) } - \frac{3( \sqrt{5} - \sqrt{2} ) }{( \sqrt{5} + \sqrt{2} )( \sqrt{5} - \sqrt{2}) }$

$\\ \implies \sf \: \frac{2( \sqrt{5} - \sqrt{3} )}{(5 - 3)} + \frac{1( \sqrt{3} - \sqrt{2}) }{(3 - 2)} - \frac{3( \sqrt{5} - \sqrt{2} ) }{(5 - 2)}$

$\\ \implies \sf \: \cancel \frac{2}{2} ( \sqrt{5} - \sqrt{3} ) + 1( \sqrt{3} - \sqrt{2} ) - \cancel \frac{3}{3} ( \sqrt{5} - \sqrt{2} )$

$\\ \implies \sf \: \cancel{\sqrt{5} }- \cancel{ \sqrt{3}} + \cancel{\sqrt{3} } - \cancel {\sqrt{2} } - \cancel { \sqrt{5} } + \cancel{\sqrt{2} }$

$\implies \boxed{ \sf{0}}$

The value comes from this expression is 0

Answer 2

Step-by-step explanation:

Given :

•Simplify:

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

To Find:

• The values from this expression =?

Formula :

It is easy to simplify by using rationalizing method :

$\\ \bullet \tt \: \frac{numerator}{denominator} \times \frac{denominator}{denominator}$

Solution :

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

By rationalizing :

$\\ \\ \implies \sf \: \frac{2( \sqrt{5} - \sqrt{3} ) }{( \sqrt{5} + \sqrt{3})( \sqrt{5} - \sqrt{3} )} + \frac{1( \sqrt{3} - \sqrt{2} )}{( \sqrt{3} + \sqrt{2})( \sqrt{3} - \sqrt{2} ) } - \frac{3( \sqrt{5} - \sqrt{2} ) }{( \sqrt{5} + \sqrt{2} )( \sqrt{5} - \sqrt{2}) }$

$\\ \implies \sf \: \frac{2( \sqrt{5} - \sqrt{3} )}{(5 - 3)} + \frac{1( \sqrt{3} - \sqrt{2}) }{(3 - 2)} - \frac{3( \sqrt{5} - \sqrt{2} ) }{(5 - 2)}$

$\\ \implies \sf \: \cancel \frac{2}{2} ( \sqrt{5} - \sqrt{3} ) + 1( \sqrt{3} - \sqrt{2} ) - \cancel \frac{3}{3} ( \sqrt{5} - \sqrt{2} )$

$\\ \implies \sf \: \cancel{\sqrt{5} }- \cancel{ \sqrt{3}} + \cancel{\sqrt{3} } - \cancel {\sqrt{2} } - \cancel { \sqrt{5} } + \cancel{\sqrt{2} }$

$\implies \boxed{ \sf{0}}$

The value comes from this expression is 0