Question

simplify by rationalising the denominator
$\frac{5 + \sqrt{6} }{5 - \sqrt{6} }$
$\frac{7 + 3 \sqrt{5} }{7 - 3 \sqrt{5} }$
$\frac{2 \sqrt{3} - \sqrt{5)} }{2 \sqrt{2 } + 3 \sqrt{3} }$
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Answer 1

Hope you got it.......

Answer 2

$\frac{5 + √6}{5 - √6}$

$From \: rationalisation -$

$\frac{(5 + √6)²}{(5 - √6)(5 + √6)}$

$\frac{(25 + 6 + 10√6)}{(5)² - (√6)²}$

$\frac{(31 + 10√6)}{(25 - 6)}$

$\frac{(31 + 10√6)}{19}$

$\frac{7 + 3√5}{7 - 3√5}$

$From \: rationalisation -$

$\frac{(7 + 3√5)²}{(7 - 3√5)(7 + 3√5)}$

$\frac{(49 + 45 + 42√5)}{(7)² - (3√5)²}$

$\frac{(94 + 42√5)}{(49 - 45)}$

$\frac{(94 + 42√5)}{4}$

$\frac{(47 + 21√5)}{2}$