Question

Simplify : 3/(5 - root3) + 2/(5 + root3)

Answer 1

=3/5-√3+2/5+√3
=3(5+√3)+2(5-√3)/5² - (√3)²
=15+3√3+10-2√3/25-3
=25+√3/22

Answer 2

$\frac{3}{(5 - \sqrt{3})} + \frac{2}{(5 + \sqrt{3})} = \frac{25 + \sqrt{3}}{22}$

Given:

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

Solution:

$\frac{3}{(5 - \sqrt{3})} + \frac{2}{(5 + \sqrt{3})} = \left(\frac{3}{5 - \sqrt{3}} \times \frac{5 + \sqrt{3}}{5 + \sqrt{3}}\right) + \left(\frac{2}{5 + \sqrt{3}} \times \frac{5 - \sqrt{3}}{5 - \sqrt{3}}\right)$

$=\frac{15 + 3 \sqrt{3}}{25 - 3} + \frac{10 - 2 \sqrt{3}}{25 - 3}$

$=\frac{(15 + 3 \sqrt{3} + 10 - 2 \sqrt{3})}{22}$

$\Rightarrow \frac{3}{(5 - \sqrt{3})} + \frac{2}{(5 + \sqrt{3})} = \frac{25 + \sqrt{3}}{22}$