a: \(\frac{\sqrt{3-2\sqrt2}}{\sqrt{17-12\sqrt2}}-\frac{\sqrt{3+2\sqrt2}}{\sqrt{17+12\sqrt2}}\)
\(=\frac{\sqrt{\left(\sqrt2-1\right)^2}}{\sqrt{\left(3-2\sqrt2\right)^2}}-\frac{\sqrt{\left(\sqrt2+1\right)^2}}{\sqrt{\left(3+2\sqrt2\right)^2}}\)
\(=\frac{\sqrt2-1}{3-2\sqrt2}-\frac{\sqrt2+1}{3+2\sqrt2}\)
\(=\frac{\sqrt2-1}{\left(\sqrt2-1\right)^2}-\frac{\sqrt2+1}{\left(\sqrt2+1\right)^2}=\frac{1}{\sqrt2-1}-\frac{1}{\sqrt2+1}=\frac{\sqrt2+1-\sqrt2+1}{\left(\sqrt2-1\right)\left(\sqrt2+1\right)}=\frac{2}{2-1}=2\)
b: \(\frac{1}{\sqrt8+\sqrt7}+\sqrt{175}-\frac{6\sqrt2-4}{3-\sqrt2}\)
\(=\frac{\sqrt8-\sqrt7}{\left(\sqrt8+\sqrt7\right)\left(\sqrt8-\sqrt7\right)}+5\sqrt7-\frac{2\sqrt2\left(3-\sqrt2\right)}{3-\sqrt2}\)
\(=2\sqrt2-\sqrt7+5\sqrt7-2\sqrt2=4\sqrt7\)
