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\(\left(\sqrt{18}+\sqrt{0,5}-3\sqrt{\frac{1}{3}}\right)-\left(\sqrt{\frac{1}{8}-\sqrt{75}}\right)\)
\(=3\sqrt{2}+\frac{\sqrt{2}}{2}-\sqrt{3}-\frac{\sqrt{2}}{4}+5\sqrt{3}\)
\(=\frac{13\sqrt{2}}{4}+4\sqrt{3}\)
\(=\frac{13\sqrt{2}+16\sqrt{3}}{4}\)
\(\left(\sqrt{18}+\sqrt{0,5}-3\sqrt{\frac{1}{3}}\right)-\left(\sqrt{\frac{1}{8}}-\sqrt{75}\right)\)
\(=\left(\sqrt{2\cdot3^2}+\sqrt{\frac{1}{2}}-3\sqrt{\frac{3}{3^2}}\right)-\left(\sqrt{\frac{2}{4^2}}-\sqrt{3\cdot5^2}\right)\)
\(=\left(3\sqrt{2}+\sqrt{\frac{2}{2^2}}-3\cdot\frac{1}{3}\sqrt{3}\right)-\left(\frac{\sqrt{2}}{4}-5\sqrt{3}\right)\)
\(=3\sqrt{2}+\frac{\sqrt{2}}{2}-\sqrt{3}-\frac{\sqrt{2}}{4}+5\sqrt{3}\)
\(=\frac{12\sqrt{2}}{4}+\frac{2\sqrt{2}}{4}-\frac{\sqrt{2}}{4}-\sqrt{3}+5\sqrt{3}\)
\(=\frac{13\sqrt{2}}{4}+4\sqrt{3}=\frac{13\sqrt{2}+16\sqrt{3}}{4}\)
22) \(\frac{1}{\sqrt{5}+\sqrt{2}}+\frac{1}{\sqrt{5}-\sqrt{2}}\)
\(=\frac{\left(\sqrt{5}-\sqrt{2}\right)+\left(\sqrt{5}+\sqrt{2}\right)}{\left(\sqrt{5}+\sqrt{2}\right)\left(\sqrt{5}-\sqrt{2}\right)}\)
\(=\frac{2\sqrt{5}}{\sqrt{5^2}-\sqrt{2^2}}\)
\(=\frac{2\sqrt{5}}{5-2}=\frac{2\sqrt{5}}{3}\)