Question

√3+√7÷√3-√7 simplify​

Answer 1

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$\frac{ \sqrt{3} + \sqrt{7}}{ \sqrt{3} - \sqrt{7} }$

By rationalising-

$\frac{ \sqrt{3} + \sqrt{7}}{ \sqrt{3} - \sqrt{7} } \times \frac{ \sqrt{3} + \sqrt{7} }{ \sqrt{3} + \sqrt{7} }$

$\frac{{ (\sqrt{3} + \sqrt{7} ) }^{2} }{(\sqrt{3} + \sqrt{7})(\sqrt{3} - \sqrt{7})}$

By using the identities-

(a+b)² = a² +b² +2ab and

(a+b) (a-b) = a²- b² respectively.

$\frac{3 + 7 + 2 \sqrt{21} }{3 - 7}$

$\frac{10 + 2 \sqrt{21} }{ - 4}$

$\frac{ - 10 - 2 \sqrt{21} }{4}$

reducing the terms-

$\frac{ 5 + \sqrt{21} }{-2}$

Answer 2

$= \frac{ \sqrt{3} + \sqrt{7} }{ \sqrt{3} - \sqrt{7} }$

$= \frac{ \sqrt{3} + \sqrt{7} }{ \sqrt{3} - \sqrt{7} } \times \frac{ \sqrt{3 } + \sqrt{7} }{ \sqrt{3} + \sqrt{7} }$

$= \frac{ { (\sqrt{3} + \sqrt{7}) }^{2} }{3 - 7}$

$= \frac{3 + 2 \sqrt{21} + 7 }{ - 4}$

$= \frac{10 + 2 \sqrt{21} }{ - 4}$

$= \frac{2(5 + \sqrt{21} )}{ - 4}$

$= \frac{5 + \sqrt{21} }{ - 2}$

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