a) \(A=\left(\dfrac{1}{2}\sqrt{28}-3\sqrt{63}+2\sqrt{112}\right):\sqrt{7}\)
\(A=\left(\dfrac{1}{2}\cdot2\sqrt{7}-3\cdot3\sqrt{7}+2\cdot4\sqrt{7}\right):\sqrt{7}\)
\(A=\left(\sqrt{7}-9\sqrt{7}+8\sqrt{7}\right):\sqrt{7}\)
\(A=0:\sqrt{7}\)
\(A=0\)
b) \(B=\dfrac{4}{\sqrt{3}-1}-\dfrac{13}{4+\sqrt{3}}\)
\(B=\dfrac{4\left(\sqrt{3}+1\right)}{\left(\sqrt{3}-1\right)\left(\sqrt{3}+1\right)}-\dfrac{13\left(4-\sqrt{3}\right)}{\left(4+\sqrt{3}\right)\left(\sqrt{4}-\sqrt{3}\right)}\)
\(B=\dfrac{4\left(\sqrt{3}+1\right)}{\left(\sqrt{3}\right)^2-1^2}-\dfrac{13\left(4-\sqrt{3}\right)}{4^2-\left(\sqrt{3}\right)^2}\)
\(B=\dfrac{4\left(\sqrt{3}+1\right)}{2}-\dfrac{13\left(4-\sqrt{3}\right)}{13}\)
\(B=2\left(\sqrt{3}+1\right)-\left(4-\sqrt{3}\right)\)
\(B=2\sqrt{3}+2-4+\sqrt{3}\)
\(B=3\sqrt{3}-2\)
c) \(C=\dfrac{3}{\sqrt{7}+2}-\dfrac{4}{3-\sqrt{7}}-2\sqrt{\left(1-\sqrt{7}\right)^2}\)
\(C=\dfrac{3\left(\sqrt{7}-2\right)}{\left(\sqrt{7}+2\right)\left(\sqrt{7}-2\right)}-\dfrac{4\left(3+\sqrt{7}\right)}{\left(3+\sqrt{7}\right)\left(3-\sqrt{7}\right)}-2\left|1-\sqrt{7}\right|\)
\(C=\dfrac{3\left(\sqrt{7}-2\right)}{\left(\sqrt{7}\right)^2-2^2}-\dfrac{4\left(3+\sqrt{7}\right)}{3^2-\left(\sqrt{7}\right)^2}+2\left(1-\sqrt{7}\right)\)
\(C=\dfrac{3\left(\sqrt{7}-2\right)}{3}-\dfrac{4\left(3+\sqrt{7}\right)}{2}+2-2\sqrt{7}\)
\(C=\sqrt{7}-2-2\left(3+\sqrt{7}\right)+2-2\sqrt{7}\)
\(C=\sqrt{7}-2-6-2\sqrt{7}+2-2\sqrt{7}\)
\(C=-3\sqrt{7}-6\)
d) \(D=3\sqrt{\left(2-\sqrt{5}\right)^2}-\dfrac{1}{\sqrt{5}+1}\)
\(D=3\left|2-\sqrt{5}\right|-\dfrac{\sqrt{5}-1}{\left(\sqrt{5}+1\right)\left(\sqrt{5}-1\right)}\)
\(D=-3\left(2-\sqrt{5}\right)-\dfrac{\sqrt{5}-1}{\left(\sqrt{5}\right)^2-1}\)
\(D=-6+3\sqrt{5}-\dfrac{\sqrt{5}-1}{4}\)
\(D=\dfrac{4\left(-6+3\sqrt{5}\right)}{4}-\dfrac{\sqrt{5}-1}{4}\)
\(D=\dfrac{-24+12\sqrt{5}-\sqrt{5}+1}{4}\)
\(D=\dfrac{11\sqrt{5}-23}{4}\)
