Question

Answer 1

b: \(A=\sqrt{11-4\sqrt{7}}-\dfrac{3}{\sqrt{7}+2}\)

\(=\sqrt{\left(\sqrt{7}-2\right)^2}-\dfrac{3\left(\sqrt{7}-2\right)}{\left(\sqrt{7}+2\right)\left(\sqrt{7}-2\right)}\)

\(=\sqrt{7}-2-\sqrt{7}+2=0\)

c: \(B=\left(\dfrac{\sqrt{x}-2}{x-\sqrt{x}}+\dfrac{2}{1-\sqrt{x}}\right):\dfrac{\sqrt{x}+2}{\sqrt{x}-1}\)

\(=\left(\dfrac{\sqrt{x}-2}{\sqrt{x}\left(\sqrt{x}-1\right)}-\dfrac{2}{\sqrt{x}-1}\right)\cdot\dfrac{\sqrt{x}-1}{\sqrt{x}+2}\)

\(=\dfrac{\sqrt{x}-2-2\sqrt{x}}{\sqrt{x}\left(\sqrt{x}-1\right)}\cdot\dfrac{\sqrt{x}-1}{\sqrt{x}+2}=\dfrac{-\sqrt{x}-2}{\sqrt{x}\left(\sqrt{x}+2\right)}=-\dfrac{1}{\sqrt[]{x}}\)