a) \(P=\left(\dfrac{1}{\sqrt{x}+2}-\dfrac{1}{2-\sqrt{x}}+\dfrac{x}{x-4}\right):\left(1+\dfrac{4}{\sqrt{x}-2}\right)\)
\(P=\left(\dfrac{1}{\sqrt{x}+2}-\dfrac{-1}{\sqrt{x}-2}+\dfrac{x}{\left(\sqrt{x}+2\right)\left(\sqrt{x}-2\right)}\right):\left(1+\dfrac{4}{\sqrt{x}-2}\right)\)
\(P=\left(\dfrac{\sqrt{x}-2}{\left(\sqrt{x}+2\right)\left(\sqrt{x}-2\right)}+\dfrac{\sqrt{x}+2}{\left(\sqrt{x}+2\right)\left(\sqrt{x}-2\right)}+\dfrac{x}{\left(\sqrt{x}-2\right)\left(\sqrt{x}+2\right)}\right):\left(1-\dfrac{4}{\sqrt{x}-2}\right)\)
\(P=\left(\dfrac{\sqrt{x}-2+\sqrt{x}+2+x}{\left(\sqrt{x}+2\right)\left(\sqrt{x}-2\right)}\right):\left(\dfrac{\sqrt{x}-2-4}{\sqrt{x}-2}\right)\)
\(P=\left(\dfrac{2\sqrt{x}+x}{\left(\sqrt{x}+2\right)\left(\sqrt{x}-2\right)}\right):\left(\dfrac{\sqrt{x}-6}{\sqrt{x}-2}\right)\)
\(P=\left(\dfrac{\sqrt{x}\left(2+\sqrt{x}\right)}{\left(\sqrt{x}+2\right)\left(\sqrt{x}-2\right)}\right)\cdot\left(\dfrac{\sqrt{x}-2}{\sqrt{x}-6}\right)\)
\(P=\dfrac{\sqrt{x}}{\sqrt{x}-2}\cdot\dfrac{\sqrt{x}-2}{\sqrt{x}-6}\)
\(P=\dfrac{\sqrt{x}}{\sqrt{x}-6}\)
b) Thay \(x=9\) vào P ta có:
\(P=\dfrac{\sqrt{9}}{\sqrt{9}-6}=\dfrac{3}{3-6}=\dfrac{3}{-3}=-1\)
a: \(P=\dfrac{\sqrt{x}-2+\sqrt{x}+2+x}{x-4}:\dfrac{\sqrt{x}-2+4}{\sqrt{x}-2}\)
\(=\dfrac{x+2\sqrt{x}}{x-4}\cdot\dfrac{\sqrt{x}-2}{\sqrt{x}+2}=\dfrac{\sqrt{x}}{\sqrt{x}+2}\)
b: Khi x=9 thì P=3/(3+2)=3/5
c: \(P=\dfrac{1}{3\sqrt{x}}\)
=>3x=căn x+2
=>\(3x-\sqrt{x}-2=0\)
=>(căn x-1)(3căn x+2)=0
=>căn x-1=0
=>x=1(nhận)