a) \(P=\left(\dfrac{4\sqrt{x}}{x-4}-\dfrac{1}{\sqrt{x}+2}\right):\dfrac{3\sqrt{x}+2}{x+4\sqrt{x}+4}\)
\(P=\left[\dfrac{4\sqrt{x}}{\left(\sqrt{x}+2\right)\left(\sqrt{x}-2\right)}-\dfrac{\sqrt{x}-2}{\left(\sqrt{x}+2\right)\left(\sqrt{x}-2\right)}\right]\cdot\dfrac{\left(\sqrt{x}+2\right)^2}{3\sqrt{x}+2}\)
\(P=\dfrac{4\sqrt{x}-\sqrt{x}+2}{\left(\sqrt{x}+2\right)\left(\sqrt{x}-2\right)}\cdot\dfrac{\left(\sqrt{x}+2\right)^2}{3\sqrt{x}+2}\)
\(P=\dfrac{3\sqrt{x}+2}{\left(\sqrt{x}+2\right)\left(\sqrt{x}-2\right)}\cdot\dfrac{\left(\sqrt{x}+2\right)^2}{3\sqrt{x}+2}\)
\(P=\dfrac{\left(\sqrt{x}+2\right)^2}{\left(\sqrt{x}+2\right)\left(\sqrt{x}-2\right)}\)
\(P=\dfrac{\sqrt{x}+2}{\sqrt{x}-2}\)
b) P = 5 khi:
\(\dfrac{\sqrt{x}+2}{\sqrt{x}-2}=5\)
\(\Rightarrow\sqrt{x}+2=5\sqrt{x}-10\)
\(\Rightarrow5\sqrt{x}-\sqrt{x}=2+10\)
\(\Rightarrow4\sqrt{x}=12\)
\(\Rightarrow\sqrt{x}=3\)
\(\Rightarrow x=9\left(tm\right)\)
c) \(P< 0\) khi:
\(\dfrac{\sqrt{x}+2}{\sqrt{x}-2}< 0\)
\(\Rightarrow\sqrt{x}-2< 0\)
\(\Rightarrow\sqrt{x}< 2\)
\(\Rightarrow x< 2^2\)
\(\Rightarrow x< 4\)
Kết hợp với ĐK:
\(0\le x< 4\)
giúp e vs ạ ;-;
giúp e vs ạ :<