Question

simplify: 1+√2÷5+√3+1-√2÷√5-√3​

Answer 1

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Brainly.in

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Secondary SchoolMath 5 points

Simplify =1/√5+√3 + 1/2(√5-√3)

Ask for details Follow Report by Mnageswarraodop7d9j0 10.05.2018

Answers

DaIncredible

DaIncredible Ace

Hey friend,

Here is the answer you were looking for:

\frac{1}{ \sqrt{5} + \sqrt{3} } + \frac{1}{2( \sqrt{5} - \sqrt{3} ) } \\ \\ = \frac{1}{ \sqrt{5} + \sqrt{3} } + \frac{1}{2 \sqrt{5} - 2 \sqrt{3} } \\

On rationalizing the denominator we get,

= \frac{1}{ \sqrt{5} + \sqrt{3} } \times \frac{ \sqrt{5} - \sqrt{3} }{ \sqrt{5} - \sqrt{3} } + \frac{1}{2 \sqrt{5} - 2 \sqrt{3} } \times \frac{2 \sqrt{5} + 2 \sqrt{3} }{2 \sqrt{5} + 2 \sqrt{3} }

Using the identity :

(x + y)(x - y) = {x}^{2} - {y}^{2}

= \frac{ \sqrt{5} - \sqrt{3} }{ {( \sqrt{5} )}^{2} - {( \sqrt{3} )}^{2} } - \frac{2 \sqrt{5} + 2 \sqrt{3} }{ {(2 \sqrt{5} })^{2} - {(2 \sqrt{3} )}^{2} } \\ \\ = \frac{ \sqrt{5} - \sqrt{3} }{5 - 3} - \frac{2 \sqrt{5} + 2 \sqrt{3} }{20 - 12} \\ \\ = \frac{ \sqrt{5} - \sqrt{3} }{2} - \frac{2 \sqrt{5} + 2 \sqrt{3} }{8} \\ \\ = \frac{ \sqrt{5} - \sqrt{3} }{2} - \frac{ \sqrt{5} + \sqrt{3} }{4} \\ \\ = \frac{ \sqrt{5} \times 2 - \sqrt{3} \times 2 - ( \sqrt{5} + \sqrt{3} )}{4} \\ \\ = \frac{2 \sqrt{5} - 2 \sqrt{3} - \sqrt{5} - \sqrt{3} }{4} \\ \\ = \frac{ \sqrt{5} - 3 \sqrt{3} }{4}