Question

# Simplify: (i) $\frac{5+\sqrt{3}}{5-\sqrt{3}}+\frac{5-\sqrt{3}}{5+\sqrt{3}}$ (ii) $\frac{1}{2+\sqrt{3}}+\frac{2}{\sqrt{5}-\sqrt{3}}+\frac{1}{2-\sqrt{5}}$ (iii) $\frac{2}{\sqrt{5}+\sqrt{3}}+\frac{1}{\sqrt{3}+\sqrt{2}}+\frac{3}{\sqrt{5}+\sqrt{2}}$

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Solution

## (i) We know that rationalization factor forand areand respectively. We will multiply numerator and denominator of the given expression and by and respectively, to get Hence the given expression is simplified to. (ii) We know that rationalization factor forand areand respectively. We will multiply numerator and denominator of the given expression and by and respectively, to get Hence the given expression is simplified to. (iii) We know that rationalization factor forand areand respectively. We will multiply numerator and denominator of the given expression and by and respectively, to get Hence the given expression is simplified to.

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