Question

Answer 1

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

Answer 2

\(\Rightarrow B=\dfrac{x-4-x+2\sqrt{x}}{x-4}.\dfrac{\sqrt{x}+2}{x}\)

\(\Rightarrow B=\dfrac{2\sqrt{x}-4}{\left(\sqrt{x}-2\right)\left(\sqrt{x}+2\right)}.\dfrac{\sqrt{x}+2}{x}\)

\(\Rightarrow B=\dfrac{2\left(\sqrt{x}-2\right)}{\left(\sqrt{x}-2\right)\left(\sqrt{x}+2\right)}.\dfrac{\sqrt{x}+2}{x}\)

\(\Rightarrow B=\dfrac{2}{x}\)