Simplify: frac{2}{sqrt{5}-sqrt{3}} + frac{4}{ | vedclass

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(B) Step $1$: Rationalize the first term $\frac{2}{\sqrt{5}-\sqrt{3}}$.Multiply numerator and denominator by $(\sqrt{5} + \sqrt{3})$:$\frac{2(\sqrt{5}

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(B) Step $1$: Rationalize the first term $\frac{2}{\sqrt{5}-\sqrt{3}}$.Multiply numerator and denominator by $(\sqrt{5} + \sqrt{3})$:$\frac{2(\sqrt{5} + \sqrt{3})}{5 - 3} = \frac{2(\sqrt{5} + \sqrt{3})}{2} = \sqrt{5} + \sqrt{3}$.Step $2$: Simplify the second term $\frac{4}{\sqrt{10+\sqrt{84}}}$.Note that $\sqrt{84} = \sqrt{4 	imes 21} = 2\sqrt{21}$.So,$\sqrt{10 + 2\sqrt{21}} = \sqrt{(\sqrt{7} + \sqrt{3})^2} = \sqrt{7} + \sqrt{3}$.Thus,the term becomes $\frac{4}{\sqrt{7} + \sqrt{3}}$.Rationalize it: $\frac{4(\sqrt{7} - \sqrt{3})}{7 - 3} = \frac{4(\sqrt{7} - \sqrt{3})}{4} = \sqrt{7} - \sqrt{3}$.Step $3$: Rationalize the third term $\frac{2}{\sqrt{7}-\sqrt{5}}$.Multiply numerator and denominator by $(\sqrt{7} + \sqrt{5})$:$\frac{2(\sqrt{7} + \sqrt{5})}{7 - 5} = \frac{2(\sqrt{7} + \sqrt{5})}{2} = \sqrt{7} + \sqrt{5}$.Step $4$: Combine all terms:$(\sqrt{5} + \sqrt{3}) + (\sqrt{7} - \sqrt{3}) - (\sqrt{7} + \sqrt{5})$$= \sqrt{5} + \sqrt{3} + \sqrt{7} - \sqrt{3} - \sqrt{7} - \sqrt{5} = 0$.

Simplify: $\frac{2}{\sqrt{5}-\sqrt{3}} + \frac{4}{\sqrt{10+\sqrt{84}}} - \frac{2}{\sqrt{7}-\sqrt{5}}$

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