Question

simplify √5+√3/√5-√3 +√5-√3/√5+√3 by rationalizing the denominator​

Answer 1

${\huge{\underline{\mathcal{\purple{Solution}}}}}$

Step-by-step explanation:

$\frac{ \sqrt{5} + \sqrt{3} }{ \sqrt{5} - \sqrt{3} } + \frac{ \sqrt{5} - \sqrt{3} }{ \sqrt{5} + \sqrt{3} } \\ = \frac{ \sqrt{8} }{ \sqrt{2} } + \frac{ \sqrt{2} }{ \sqrt{8} } \\ = \frac{ \sqrt{16} + \sqrt{2} }{ \sqrt{8} } \\ = \frac{4 + \sqrt{2} }{ \sqrt{8} } \\ now \: rationalising \\ = \frac{4 + \sqrt{2} }{ \sqrt{8} } \times \frac{ \sqrt{8} }{ \sqrt{8} } \\ = \frac{4 \sqrt{8} + \sqrt{16} }{ ({ \sqrt{8} })^{2} } \\ = \frac{4 \sqrt{8} + 4}{8} \\ = \sqrt{8} + 2$

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