Question

rationalize the denominator 2√5 -√3/ 2√5 +√3
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Answer 1

$\color{red}{ANSWER :-}$

$\frac{2\sqrt{5}-\sqrt{3}}{2\sqrt{5}+\sqrt{3}}$

$\bf{lets \: rationalize} \\ = )\frac{2 \sqrt{5} - \sqrt{3} }{2 \sqrt{5} + \sqrt{3} } \times \frac{2 \sqrt{5} - \sqrt{3} }{2 \sqrt{5} - \sqrt{3} } \\ \frac{(x - y)(x - y) = {x}^{2} - 2xy + {y}^{2} }{(x + y)(x - y) = {x}^{2} - {y}^{2} } \\ = ) \frac{(2 \sqrt{5} {)}^{2} - (2 \times 2 \sqrt{5} \times \sqrt{3}) + ( \sqrt{ {3} } {)}^{2} }{ ({2 \sqrt{5}) }^{2} - { (\sqrt{3} )}^{2} } \\ = ) \frac{(4 \times 5) - 4 \sqrt{15} + 3 }{(4 \times 5) - 3} \\ = ) \frac{20 - 4 \sqrt{15} + 3}{20 - 3} \\ = ) \boxed{ \frac{23 - 4 \sqrt{15} }{17} }$

$\color{Orange}{Hope \: it\: helped}$