a) \(A=\left(3\sqrt{18}+2\sqrt{50}-4\sqrt{72}\right):8\sqrt{2}\)
\(A=\left(3\cdot3\sqrt{2}+2\cdot5\sqrt{2}-4\cdot6\sqrt{2}\right):8\sqrt{2}\)
\(A=\left(9\sqrt{2}+10\sqrt{2}-24\sqrt{2}\right):8\sqrt{2}\)
\(A=-5\sqrt{2}:8\sqrt{2}\)
\(A=-\dfrac{5}{8}\)
\(b,B=\left(-4\sqrt{20}+5\sqrt{500}-3\sqrt{45}\right):\sqrt{5}\\ B=\left(-4\sqrt{2^2.5}+5.\sqrt{5.10^2}-3.\sqrt{3^2.5}\right):\sqrt{5}\\ =\left(-4.2\sqrt{5}+5.10\sqrt{5}-3.3\sqrt{5}\right):\sqrt{5}\\ =-8+50-9=33\)
\(C=\left(\dfrac{\sqrt{3}+1}{\sqrt{3}-1}-\dfrac{\sqrt{3}-1}{\sqrt{3}+1}\right):\sqrt{48}\\ =\left[\dfrac{\left(\sqrt{3}+1\right)^2-\left(\sqrt{3}-1\right)^2}{3-1}\right]:\sqrt{4^2.3}\\ =\dfrac{\left(\sqrt{3}+1-\sqrt{3}+1\right).\left(\sqrt{3}+1+\sqrt{3}-1\right)}{2}:4\sqrt{3}\\ =\dfrac{2.2\sqrt{3}}{2}:4\sqrt{3}=\dfrac{2\sqrt{3}}{4\sqrt{3}}=\dfrac{1}{2}\)
b) \(B=\left(-4\sqrt{20}+5\sqrt{500}-3\sqrt{45}\right):\sqrt{5}\)
\(B=\left(-4\cdot2\sqrt{5}+5\cdot10\sqrt{5}-3\cdot3\sqrt{5}\right):\sqrt{5}\)
\(B=\left(-8\sqrt{2}+50\sqrt{5}-9\sqrt{5}\right):\sqrt{5}\)
\(B=33\sqrt{5}:\sqrt{5}\)
\(B=33\)
c) \(C=\left(\dfrac{\sqrt{3}+1}{\sqrt{3}-1}-\dfrac{\sqrt{3}-1}{\sqrt{3}+1}\right):\sqrt{48}\)
\(C=\dfrac{\left(\sqrt{3}+1\right)^2-\left(\sqrt{3}-1\right)^2}{\left(\sqrt{3}-1\right)\left(\sqrt{3}+1\right)}:4\sqrt{3}\)
\(C=\dfrac{3+2\sqrt{3}+1-3+2\sqrt{3}-1}{3-1}:4\sqrt{3}\)
\(C=\dfrac{4\sqrt{3}}{2}:4\sqrt{3}\)
\(C=2\sqrt{3}:4\sqrt{3}\)
\(C=\dfrac{1}{2}\)
