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

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(B) To simplify the expression,we rationalize each term individually.First term: $\frac{2 \sqrt{2}}{\sqrt{5}+\sqrt{3}} = \frac{2 \sqrt{2}(\sqrt{5}-\sq

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(B) To simplify the expression,we rationalize each term individually.First term: $\frac{2 \sqrt{2}}{\sqrt{5}+\sqrt{3}} = \frac{2 \sqrt{2}(\sqrt{5}-\sqrt{3})}{5-3} = \frac{2(\sqrt{10}-\sqrt{6})}{2} = \sqrt{10}-\sqrt{6}$.Second term: $\frac{3 \sqrt{3}}{\sqrt{5}+\sqrt{2}} = \frac{3 \sqrt{3}(\sqrt{5}-\sqrt{2})}{5-2} = \frac{3(\sqrt{15}-\sqrt{6})}{3} = \sqrt{15}-\sqrt{6}$.Third term: $\frac{\sqrt{5}}{\sqrt{3}+\sqrt{2}} = \frac{\sqrt{5}(\sqrt{3}-\sqrt{2})}{3-2} = \sqrt{15}-\sqrt{10}$.Now,substitute these back into the original expression:$(\sqrt{10}-\sqrt{6}) - (\sqrt{15}-\sqrt{6}) + (\sqrt{15}-\sqrt{10})$$= \sqrt{10} - \sqrt{6} - \sqrt{15} + \sqrt{6} + \sqrt{15} - \sqrt{10}$$= 0$.

Simplify: $\frac{2 \sqrt{2}}{\sqrt{5}+\sqrt{3}}-\frac{3 \sqrt{3}}{\sqrt{5}+\sqrt{2}}+\frac{\sqrt{5}}{\sqrt{3}+\sqrt{2}}$

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