Question

plz solve it guys and help

Answer 1

$\frac{ \sqrt{5 } + \sqrt{3} }{ \sqrt{80} + \sqrt{48} - \sqrt{45} - \sqrt{27} }$
=
$\frac{ \sqrt{5} + \sqrt{3} }{4 \sqrt{5} + 4 \sqrt{3} - 3 \sqrt{5} - 3 \sqrt{3} }$


= $\frac{ \sqrt{5} + \sqrt{3} }{4 \sqrt{5} - 3 \sqrt{5} + 4 \sqrt{3} - 3 \sqrt{3} }$
Now do some calculations and you'll get
$= \frac{ \sqrt{5} + \sqrt{3} }{ \sqrt{5} - \sqrt{3} }$
Now rationalize the terms and you'll get
$\frac{ \sqrt{5} + \sqrt{3} }{ \sqrt{5} - \sqrt{3} } \times \frac{ \sqrt{5} + \sqrt{3} }{ \sqrt{5} + \sqrt{3} } \\ = \frac{5 + 3 + 2 \sqrt{15} }{5 - 3} = \frac{8 + 2 \sqrt{15} }{2}$

take 2 common on the numerator and you'll get
$\frac{2(4 + \sqrt{15)} }{2} \\ = 4 + \sqrt{15}$