Question

Simplify 2-√7 / √5+√3​

Answer 1

$\large\bf\underline\red{Answer \: :-}$

This type of example we solve by ‘Rationalizing’ also we know ‘Rationalize the denominator’.

$\sf:\implies{ \frac{2 - \sqrt{7} }{ \sqrt{5} + 3} \times \frac{ \sqrt{5} - 3}{ \sqrt{5} - 3 } } \\ \\ \sf:\implies{ \frac{(2 - \sqrt{7} )( \sqrt{5} - 3)}{( \sqrt{5} + 3)( \sqrt{5} - 3) } } \\ \\ \sf:\implies{ \frac{2(\sqrt{5} - 3) - \sqrt{7} ( \sqrt{5} - 3)}{( \sqrt{5}) {}^{2} - (3) {}^{2} } } \\ \\ \sf:\implies{ \frac{2 \sqrt{5} - 6 - \sqrt{35} - 3 \sqrt{7} }{5 - 9} } \\ \\ \sf:\implies{ \frac{2 \sqrt{5} - 6 - \sqrt{35} - 3 \sqrt{7} \times ( - \sqrt{35}) }{ - 4 \times ( - \sqrt{35} )} \: \: \: ( \: \because \:multiply \: by \: - \sqrt{35} ) } \\ \\ \sf:\implies{ \boxed{ \red{\frac{2 \sqrt{5} - 41 - 3 \sqrt{7} }{4 \sqrt{35} } }}}$

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