Cho P = (\(\frac{\sqrt{x}}{\sqrt{x}-2}\)-- \(\frac{4}{x-2\sqrt{x}}\)) (\(\frac{1}{\sqrt{x}+2}\)+ \(\frac{4}{x-4}\))
với x \(\ge\)0 , x \(\ne\)4
a) Rút gọn P
b) khi x = 4+2\(\sqrt{3}\). Tính P
c) Tìm x để P dương
( Mấy bạn giúp mình với, mình đang cần gấp)
a, \(P=\frac{x-4}{\sqrt{x}\left(\sqrt{x-2}\right)}.\frac{\sqrt{x}+2}{\left(\sqrt{x}+2\right)\left(\sqrt{x}-2\right)}\)
\(=\frac{\left(\sqrt{x}+2\right)\left(\sqrt{x}-2\right)}{\sqrt{x}\left(\sqrt{x}-2\right)}.\frac{\sqrt{x}+2}{\left(\sqrt{x}+2\right)\left(\sqrt{x}-2\right)}=\frac{\sqrt{x}+2}{x-2\sqrt{x}}\)
b. Với \(x=4+2\sqrt{3}\Rightarrow P=\frac{\sqrt{4+2\sqrt{3}}+2}{4+2\sqrt{3}-2\sqrt{4+2\sqrt{3}}}\)
\(=\frac{\sqrt{3}+1+2}{4+2\sqrt{3}-2\left(\sqrt{3}+1\right)}=\frac{3+\sqrt{3}}{2}\)
C. \(P>0\Rightarrow\frac{\sqrt{x}+2}{x-2\sqrt{x}}>0\Rightarrow x-2\sqrt{x}>0\Rightarrow x>4\)