\(P=\left(\dfrac{4\sqrt{x}}{\sqrt{x}+2}-\dfrac{8x}{x-4}\right):\left(\dfrac{\sqrt{x}+2}{\sqrt{x}-2}+3\right)\\ =\left(\dfrac{4\sqrt{x}\left(\sqrt{x}-2\right)-8x}{x-4}\right):\left(\dfrac{\sqrt{x}+2+3\left(\sqrt{x}-2\right)}{\sqrt{x}-2}\right)\\ =\left(\dfrac{4x-8\sqrt{x}-8x}{x-4}\right)\times\left(\dfrac{\sqrt{x}-2}{\sqrt{x}+2+3\sqrt{x}-6}\right)\\ =\left(\dfrac{-8\sqrt{x}-4x}{x-4}\right)\times\left(\dfrac{\sqrt{x}-2}{4\sqrt{x}-4}\right)\\ =\left(\dfrac{-4\sqrt{x}\left(2+\sqrt{x}\right)}{\left(2+\sqrt{x}\right)\left(\sqrt{x}-2\right)}\right)\times\left(\dfrac{\sqrt{x}-2}{4\left(\sqrt{x}-1\right)}\right)\)
\(=\dfrac{-4\sqrt{x}}{4\left(\sqrt{x}-1\right)}=\dfrac{-\sqrt{x}}{\sqrt{x}-1}\)
b, \(P=-4\\ \Rightarrow\dfrac{-\sqrt{x}}{\sqrt{x}-1}=-4\\ \Leftrightarrow-\sqrt{x}=-4\sqrt{x}+4\\ \Leftrightarrow-\sqrt{x}+4\sqrt{x}=4\\ \Leftrightarrow\sqrt{x}=\dfrac{4}{3}\\ \Rightarrow x=\dfrac{16}{9}\left(t/mđk\right)\)
a) \(P=\left(\dfrac{4\sqrt{x}}{\sqrt{x}+2}-\dfrac{8x}{x-4}\right):\left(\dfrac{\sqrt{x}+2}{\sqrt{x}-2}+3\right)\) (ĐK: \(x\ne4;x\ge0\))
\(P=\left[\dfrac{4\sqrt{x}\left(\sqrt{x}-2\right)}{\left(\sqrt{x}+2\right)\left(\sqrt{x}-2\right)}-\dfrac{8x}{\left(\sqrt{x}+2\right)\left(\sqrt{x}-2\right)}\right]:\dfrac{\sqrt{x}+2+3\left(\sqrt{x}-2\right)}{\sqrt{x}-2}\)
\(P=\dfrac{4x-8\sqrt{x}-8x}{\left(\sqrt{x}+2\right)\left(\sqrt{x}-2\right)}:\dfrac{\sqrt{x}+2+3\sqrt{x}-6}{\sqrt{x}-2}\)
\(P=\dfrac{-4x-8\sqrt{x}}{\left(\sqrt{x}-2\right)\left(\sqrt{x}+2\right)}:\dfrac{4\sqrt{x}-4}{\sqrt{x}-2}\)
\(P=\dfrac{-4\sqrt{x}\left(\sqrt{x}+2\right)}{\left(\sqrt{x}-2\right)\left(\sqrt{x}+2\right)}\cdot\dfrac{\sqrt{x}-2}{4\sqrt{x}-4}\)
\(P=\dfrac{-4\sqrt{x}}{4\sqrt{x}-4}\)
\(P=\dfrac{\sqrt{x}}{1-\sqrt{x}}\)
b) \(P=-4\) khi:
\(\dfrac{\sqrt{x}}{1-\sqrt{x}}=-4\)
\(\Leftrightarrow\sqrt{x}=-4+4\sqrt{x}\)
\(\Leftrightarrow3\sqrt{x}=4\)
\(\Leftrightarrow\sqrt{x}=\dfrac{4}{3}\)
\(\Leftrightarrow x=\dfrac{16}{9}\left(tm\right)\)
