Question

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Answer 1

a: \(A=2\sqrt3-\sqrt{75}+2\cdot\sqrt{12}\)

\(=2\sqrt3-5\sqrt3+2\cdot2\sqrt3\)

\(=6\sqrt3-5\sqrt3=\sqrt3\)

b: \(B=\sqrt{\left(2-\sqrt5\right)^2}+\sqrt{\left(3-\sqrt5\right)^2}\)

\(=\left|2-\sqrt5\right|+\left|3-\sqrt5\right|\)

\(=\sqrt5-2+3-\sqrt5=-2+3=1\)

c: \(C=\left(\frac{x+2\sqrt{x}}{x-2\sqrt{x}}+\frac{\sqrt{x}}{\sqrt{x}-2}\right)\cdot\frac{1}{\sqrt{x}+1}\)

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

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