Question

Simplify 7/(√17-2√3) - 3/(√17+2√3)

Answer 1

$\large\frac{7}{ \sqrt{17} - 2\sqrt{3} } - \frac{3}{ \sqrt{17} + 2 \sqrt{3} }$

$\large = \frac{7( \sqrt{17 } + 2 \sqrt{3} ) - 3( \sqrt{17} - 2 \sqrt{3}) }{( \sqrt{17} - 2 \sqrt{3} )( \sqrt{17} + 2 \sqrt{3}) }$

$\large = \frac{7 \sqrt{17} + 14 \sqrt{3} - 3 \sqrt{17} + 14 \sqrt{3} }{ { (\sqrt{17}) }^{2} - ({ 2\sqrt{3} })^{2} }$

$\large= \frac{4 \sqrt{17} + 28 \sqrt{3} }{ 17 - 12 }$

$\large= \frac{4 \sqrt{17} + 28 \sqrt{3} }{5}$