Question
Simplify the following$\frac{3}{5-\sqrt{3}}+\frac{2}{5+\sqrt{3}}$
✓
Answer
$\frac{3}{5-\sqrt{3}}+\frac{2}{5+\sqrt{3}}$
$=\frac{3(5+\sqrt{3})+2(5-\sqrt{3})}{(5-\sqrt{3})(5+\sqrt{3})}$
$=\frac{15+3 \sqrt{3}+10-2 \sqrt{3}}{(5)^2-(\sqrt{3})^2}$
$=\frac{25+\sqrt{3}}{25-3}$
$=\frac{25+\sqrt{3}}{22}$
$=\frac{3(5+\sqrt{3})+2(5-\sqrt{3})}{(5-\sqrt{3})(5+\sqrt{3})}$
$=\frac{15+3 \sqrt{3}+10-2 \sqrt{3}}{(5)^2-(\sqrt{3})^2}$
$=\frac{25+\sqrt{3}}{25-3}$
$=\frac{25+\sqrt{3}}{22}$
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