Question

6. Rationalize the denominator and simplify. 2+√3/5-√3

Answer 1

$\frac{2+ \sqrt{3} }{5- \sqrt{3} } = ?$
$\frac{2+ \sqrt{3} }{5- \sqrt{3} }* \frac{5+ \sqrt{3}}{5+ \sqrt{3}} =$
$\frac{(2+ \sqrt{3})*(5+ \sqrt{3}) }{(5- \sqrt{3})*(5+ \sqrt{3} )} =$
$\frac{10+2 \sqrt{3}+5 \sqrt{3}+ \sqrt{3} ^{2} }{25+5 \sqrt{3}-5 \sqrt{3} -\sqrt{3} ^{2} } =$
$\frac{10+7 \sqrt{3}+3}{25-3} =$
$\boxed{\frac{13+7 \sqrt{3}}{22} or13,55110708...}$