\(a)\dfrac{1}{3+\sqrt{2}}+\dfrac{1}{3-\sqrt{2}}\)
\(=\dfrac{\left(3-\sqrt{2}\right)+\left(3+\sqrt{2}\right)}{\left(3+\sqrt{2}\right)\left(3-\sqrt{2}\right)}\)
\(=\dfrac{3-\sqrt{2}+3+\sqrt{2}}{9-2}\)
\(=\dfrac{6}{7}\)
\(b)\dfrac{2}{3\sqrt{2}-4}-\dfrac{2}{3\sqrt{2}+4}\)
\(=\dfrac{2\left(3\sqrt{2}+4\right)-2\left(3\sqrt{2}-4\right)}{\left(3\sqrt{2}-4\right)\left(3\sqrt{2}+4\right)}\)
\(=\dfrac{2.\left[\left(3\sqrt{2}+4\right)-\left(3\sqrt{2}-4\right)\right]}{18-16}\)
\(=\dfrac{2\left(3\sqrt{2}+4-3\sqrt{2}+4\right)}{2}\)
\(=\dfrac{16}{2}\)
\(=8\)
\(c)\dfrac{\sqrt{5}-\sqrt{3}}{\sqrt{5}+\sqrt{3}}+\dfrac{\sqrt{5}+\sqrt{3}}{\sqrt{5}-\sqrt{3}}\)
\(=\dfrac{\left(\sqrt{5}-\sqrt{3}\right)\left(\sqrt{5}-\sqrt{3}\right)+\left(\sqrt{5}+\sqrt{3}\right)\left(\sqrt{5}+\sqrt{3}\right)}{\left(\sqrt{5}+\sqrt{3}\right)\left(\sqrt{5}-\sqrt{3}\right)}\)
\(=\dfrac{\left(\sqrt{5}-\sqrt{3}\right)^2+\left(\sqrt{5}+\sqrt{3}\right)^2}{5-3}\)
\(=\dfrac{5-2\sqrt{15}+3+5+2\sqrt{15}+3}{2}\)
\(=\dfrac{8+8}{2}\)
\(=\dfrac{16}{2}\)
\(=8\)
a: \(=\dfrac{3-\sqrt{2}+3+\sqrt{2}}{9-2}=\dfrac{6}{7}\)
b: \(=\dfrac{2\left(3\sqrt{2}+4\right)-2\left(3\sqrt{2}-4\right)}{18-16}\)
=3căn 2+4-3căn 2+4
=8
c: \(=\dfrac{\left(\sqrt{5}-\sqrt{3}\right)^2+\left(\sqrt{5}+\sqrt{3}\right)^2}{2}\)
\(=\dfrac{8-2\sqrt{15}+8+2\sqrt{15}}{2}=\dfrac{16}{2}=8\)
