Lời giải:
a) \(A=\sqrt{(\sqrt{3}-\sqrt{5})^2}-\sqrt{(\sqrt{3}+\sqrt{5})^2}\)
\(=|\sqrt{3}-\sqrt{5}|-|\sqrt{3}+\sqrt{5}|\)
\(=\sqrt{5}-\sqrt{3}-(\sqrt{3}+\sqrt{5})\)
\(=-2\sqrt{3}\)
b) \(B=\frac{\sqrt{9x^2-6x+1}}{9x^2-1}=\frac{\sqrt{(3x-1)^2}}{(3x-1)(3x+1)}\)
\(=\frac{|3x-1|}{(3x-1)(3x+1)}\)
Nếu \(x> \frac{1}{3}\Rightarrow B=\frac{3x-1}{(3x-1)(3x+1)}=\frac{1}{3x+1}\)
Nếu \(x< \frac{1}{3}; x\neq \frac{-1}{3}\) thì \(B=\frac{1-3x}{(3x-1)(3x+1)}=\frac{-1}{3x+1}\)
c) \(C=\sqrt{7+4\sqrt{3}}-\sqrt{7-4\sqrt{3}}\)
\(=\sqrt{3+4+2\sqrt{3.4}}-\sqrt{3+4-2\sqrt{3.4}}\)
\(=\sqrt{(\sqrt{3}+2)^2}-\sqrt{(\sqrt{3}-2)^2}\)
\(=|\sqrt{3}+2|-|\sqrt{3}-2|=\sqrt{3}+2-(2-\sqrt{3})\)
\(=2\sqrt{3}\)
