1/ \(A=\dfrac{x}{x-4}+\dfrac{1}{\sqrt{x}-2}+\dfrac{1}{\sqrt{x}+2}\)
\(=\dfrac{x}{x-4}+\dfrac{\sqrt{x}+2}{x-4}+\dfrac{\sqrt{x}-2}{x-4}=\dfrac{x+2\sqrt{x}}{x-4}\)
\(=\dfrac{\sqrt{x}\left(\sqrt{x}+2\right)}{\left(\sqrt{x}-2\right)\left(\sqrt{x}+2\right)}=\dfrac{\sqrt{x}}{\sqrt{x}-2}\)
2/ Khi x = 25 thì:
\(A=\dfrac{\sqrt{25}}{\sqrt{25}-2}=\dfrac{5}{5-2}=\dfrac{5}{3}\)
3/ A = \(-\dfrac{1}{3}\)
\(\Leftrightarrow\dfrac{\sqrt{x}}{\sqrt{x}-2}=-\dfrac{1}{3}\)
\(\Leftrightarrow\sqrt{x}=-\dfrac{1}{3}\sqrt{x}+\dfrac{2}{3}\)
\(\Leftrightarrow\sqrt{x}+\dfrac{1}{3}\sqrt{x}=\dfrac{2}{3}\)
\(\Leftrightarrow\dfrac{4}{3}\sqrt{x}=\dfrac{2}{3}\Leftrightarrow\sqrt{x}=\dfrac{1}{2}\Leftrightarrow x=\dfrac{1}{4}\left(tm\right)\)
vậy............