Question

Find the sum of the expression (1/root1+root2)+(1/root2+root3)

Answer 1

Hey friend,
Here is the answer you were looking for:
$( \frac{1}{ ( \sqrt{1}) + (\sqrt{2} ) } ) + ( \frac{1}{( \sqrt{2}) + ( \sqrt{3}) } ) \\ \\ first \: rationalizing \: we \: get \\ \\ = ( \frac{1}{ \sqrt{1} + \sqrt{2} } ) \times \frac{ \sqrt{1} - \sqrt{2} }{ \sqrt{1} - \sqrt{2} } \\ + ( \frac{1}{ \sqrt{2} + \sqrt{3} } ) \times \frac{ \sqrt{2} - \sqrt{3} }{ \sqrt{2} - \sqrt{3} } \\ \\ = \frac{ \sqrt{1} - \sqrt{2} }{1 - 2} + \frac{ \sqrt{2} - \sqrt{3} }{2 - 3} \\ \\ = \frac{ \sqrt{1} - \sqrt{2} }{ - 1} + \frac{ \sqrt{2} - \sqrt{3} }{ - 1} \\ \\ ( - \sqrt{1} + \sqrt{2} ) + ( - \sqrt{2} + \sqrt{3} ) \\ \\ = - \sqrt{1} + \sqrt{2} - \sqrt{2} + \sqrt{3} \\ \\ = - \sqrt{1} + \sqrt{3}$

Hope this helps!!!

@Mahak24

Thanks...
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