\(a,ĐKXĐ:x\ge0;x\ne4\)

Ta có: \(P=\frac{\sqrt{x}+1}{\sqrt{x}-2}+\frac{2\sqrt{x}}{\sqrt{x}+2}-\frac{5\sqrt{x}+2}{x-4}\)

\(=\frac{\left(\sqrt{x}+1\right)\left(\sqrt{x}+2\right)}{\left(\sqrt{x}-2\right)\left(\sqrt{x}+2\right)}+\frac{2\sqrt{x}\left(\sqrt{x}-2\right)}{\left(\sqrt{x}+2\right)\left(\sqrt{x}-2\right)}-\frac{5\sqrt{x}+2}{\left(\sqrt{x}-2\right)\left(\sqrt{x}+2\right)}\)

\(=\frac{x+2\sqrt{x}+\sqrt{x}+2}{\left(\sqrt{x}-2\right)\left(\sqrt{x}+2\right)}+\frac{2x-4\sqrt{x}}{\left(\sqrt{x}+2\right)\left(\sqrt{x}-2\right)}-\frac{5\sqrt{x}+2}{\left(\sqrt{x}-2\right)\left(\sqrt{x}+2\right)}\)

\(=\frac{x+3\sqrt{x}+2+2x-4\sqrt{x}-5\sqrt{x}-2}{\left(\sqrt{x}-2\right)\left(\sqrt{x}+2\right)}\)

\(=\frac{3x-6\sqrt{x}}{\left(\sqrt{x}-2\right)\left(\sqrt{x}+2\right)}\)

\(=\frac{3\sqrt{x}\left(\sqrt{x}-2\right)}{\left(\sqrt{x}-2\right)\left(\sqrt{x}+2\right)}\)

\(=\frac{3\sqrt{x}}{\sqrt{x}+2}\)

Vậy....

\(b,ĐKXĐ:x\ge0;x\ne4\)

\(ĐểP=2\Rightarrow\frac{3\sqrt{x}}{\sqrt{x}+2}=2\)

\(\Leftrightarrow2\left(\sqrt{x}+2\right)=3\sqrt{x}\)

\(\Leftrightarrow3\sqrt{x}=2\sqrt{x}+4\)

\(\Leftrightarrow3\sqrt{x}-2\sqrt{x}=4\)

\(\Leftrightarrow\sqrt{x}=4\)

\(\Leftrightarrow x=16\text{(Thỏa mãn ĐKXĐ)}\)

Vậy...

a) 

\(P=\frac{\sqrt{x}+1}{\sqrt{x}-2}+\frac{2\sqrt{x}}{\sqrt{x}+2}-\frac{5\sqrt{x}+2}{x-4}\)

\(P=\frac{\left(\sqrt{x}+1\right)\left(\sqrt{x}+2\right)}{\left(\sqrt{x}-2\right)\left(\sqrt{x}+2\right)}+\frac{2\sqrt{x}\left(\sqrt{x}-2\right)}{\left(\sqrt{x}-2\right)\left(\sqrt{x}+2\right)}-\frac{2+5\sqrt{x}}{\left(\sqrt{x}-2\right)\left(\sqrt{x}+2\right)}\)

\(P=\frac{x+3\sqrt{x}+2+2x-4\sqrt{x}-2-5\sqrt{x}}{\left(\sqrt{x}-2\right)\left(\sqrt{x}+2\right)}\)

\(P=\frac{3x-6\sqrt{x}}{\left(\sqrt{x}-2\right)\left(\sqrt{x}+2\right)}=\frac{3\sqrt{x}\left(\sqrt{x}-2\right)}{\left(\sqrt{x}-2\right)\left(\sqrt{x}+2\right)}=\frac{3\sqrt{x}}{\sqrt{x}+2}\)

b) Thay P = 2 vào , ta được :

\(2=\frac{3\sqrt{x}}{\sqrt{x}+2}\Leftrightarrow2\sqrt{x}+4=3\sqrt{x}\)

\(\Leftrightarrow\sqrt{x}=4\Leftrightarrow x=16\)

Vậy x = 16 thì P = 2

a=căn (x)

A=[(4-a^2)(2-a)+2a(4-a^2)-4a^2(2-a)]/[(4-a^2)(2-a)2a]

A=(8-10a^2+4a+3a^3)/a(16-4a^2-8a+2a^3)

A=(a-2)^2(3a+2)/a(a+2)(a-2)^2*2

A=(3a+2)/a(a+2)*2

B=2+căn(3)

A=B suy ra

(3a+2)/a(a+2)*2=2+căn 3

<=>bấm máy tính ra nghiệm a=0.1539181357

=>x=a^2 =0.02341454985

tl đúng

Làm sương sương :))

\(P=\frac{\sqrt{x}+1}{\sqrt{x}-2}+\frac{2\sqrt{x}}{\sqrt{x}+2}-\frac{5\sqrt{x}+2}{x-4}\)

\(P=\frac{\left(\sqrt{x}+1\right)\left(\sqrt{x}+2\right)+2\sqrt{x}\left(\sqrt{x}-2\right)}{\left(\sqrt{x}-2\right)\left(\sqrt{x}+2\right)}-\frac{5\sqrt{x}+2}{x-4}\)

\(P=\frac{x+2\sqrt{x}+\sqrt{x}+2+2x-4\sqrt{x}-5\sqrt{x}-2}{\left(\sqrt{x}-2\right)\left(\sqrt{x}+2\right)}\)

\(P=\frac{3x-6\sqrt{x}}{\left(\sqrt{x}-2\right)\left(\sqrt{x}+2\right)}=\frac{3\sqrt{x}\left(\sqrt{x}-2\right)}{\left(\sqrt{x}-2\right)\left(\sqrt{x}+2\right)}=\frac{3\sqrt{x}}{\sqrt{x}+2}\)

Để P = 2 thì \(\frac{3\sqrt{x}}{\sqrt{x}+2}=2\Rightarrow\frac{3\sqrt{x}}{\sqrt{x}+2}-2=0\)

\(\Rightarrow\frac{3\sqrt{x}-2\left(\sqrt{x}+2\right)}{\sqrt{x}+2}=0\Rightarrow\frac{3\sqrt{x}-2\sqrt{x}-4}{\sqrt{x}+2}=0\)

\(\Rightarrow\frac{\sqrt{x}-4}{\sqrt{x}+2}=0\Rightarrow\sqrt{x}-4=0\)

\(\Leftrightarrow x=16\)

\(đkxđ\Leftrightarrow\hept{\begin{cases}x\ge0\\\sqrt{x}-1\ne0\end{cases}\Rightarrow\hept{\begin{cases}x\ge0\\\sqrt{x}\ne1\end{cases}\Rightarrow}\hept{\begin{cases}x\ge0\\x\ne1\end{cases}}}\)

\(M=\frac{\sqrt{x}}{\sqrt{x}-1}+\frac{3}{\sqrt{x}+1}-\frac{6\sqrt{x}-4}{x-1}.\)

\(=\frac{\sqrt{x}\left(\sqrt{x}+1\right)}{x-1}+\frac{3\left(\sqrt{x}-1\right)}{x-1}-\frac{6\sqrt{x}-4}{x-1}\)

\(=\frac{x+\sqrt{x}+3\sqrt{x}-3-6\sqrt{x}+4}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)}\)

\(=\frac{x-2\sqrt{x}+1}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)}=\frac{\left(\sqrt{x}-1\right)^2}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)}=\frac{\sqrt{x}-1}{\sqrt{x}+1}\)

\(b,M< \frac{1}{2}\Leftrightarrow\frac{\sqrt{x}-1}{\sqrt{x}+1}< \frac{1}{2}\)

\(\Rightarrow\frac{\sqrt{x}-1}{\sqrt{x}+1}-\frac{1}{2}< 0\)\(\Rightarrow\frac{2\left(\sqrt{x}-1\right)}{2\left(\sqrt{x}+1\right)}-\frac{\sqrt{x}+1}{2\left(\sqrt{x}+1\right)}< 0\)

\(\Rightarrow\frac{2\sqrt{x}-1-\sqrt{x}-1}{2\left(\sqrt{x}+1\right)}< 0\)\(\Rightarrow\frac{\sqrt{x}-2}{2\left(\sqrt{x}+1\right)}< 0\)

Vì \(2\left(\sqrt{x}+1\right)>0\Rightarrow\sqrt{x}-2>0\Rightarrow\sqrt{x}>2\)

\(\Rightarrow\sqrt{x}>\sqrt{4}\Leftrightarrow x>4\)

\(M=\frac{\sqrt{x}}{\sqrt{x}-1}+\frac{3}{\sqrt{x}+1}-\frac{6\sqrt{x}-4}{x-1}\left(x\ge0;x\ne1\right)\)

\(M=\frac{\sqrt{x}\left(\sqrt{x}+1\right)}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)}+\frac{3\left(\sqrt{x}-1\right)}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)}-\frac{6\sqrt{x}-4}{x-1}\)

\(M=\frac{x+\sqrt{x}+3\sqrt{x}-3}{\left(\sqrt{x}\right)^2-1^2}-\frac{6\sqrt{x}-4}{x-1}\)

\(M=\frac{x-2\sqrt{x}+1}{x-1}\)

\(M=\frac{\left(\sqrt{x}-1\right)^2}{x-1}\)

Chết , sai rồi câu b  : Vì \(2\left(\sqrt{x}+1\right)>0\Rightarrow\sqrt{x}-2< 0\)

\(\Rightarrow\sqrt{x}< 2\Rightarrow\sqrt{x}< \sqrt{4}\Rightarrow x< 4\)

a) N = \(\frac{x}{x-4}+\frac{1}{\sqrt{x}-2}+\frac{1}{\sqrt{x}+2}\)

N = \(\frac{x+\sqrt{x}+2+\sqrt{x}-2}{\left(\sqrt{x}-2\right)\left(\sqrt{x}+2\right)}\)

N = \(\frac{x+2\sqrt{x}}{\left(\sqrt{x}-2\right)\left(\sqrt{x}+2\right)}\)

N = \(\frac{\sqrt{x}\left(\sqrt{x}+2\right)}{\left(\sqrt{x}+2\right)\left(\sqrt{x}-2\right)}\)

N = \(\frac{\sqrt{x}}{\sqrt{x}-2}\)

b) Với x \(\ge\)0; x \(\ne\)4

Ta có: N = \(\frac{1}{-3}\) <=> \(\frac{\sqrt{x}}{\sqrt{x}-2}=\frac{1}{-3}\)

=> \(-3\sqrt{x}=\sqrt{x}-2\)

<=> \(-4\sqrt{x}=-2\)

<=> \(\sqrt{x}=\frac{1}{2}\)

<=> \(x=\frac{1}{4}\)

c) x = 25 => N = \(\frac{\sqrt{25}}{\sqrt{25}-2}=\frac{5}{5-3}=\frac{5}{2}\)

a) \(N=\frac{x}{x-4}+\frac{1}{\sqrt{x}-2}+\frac{1}{\sqrt{x}+2}\)

\(N=\frac{x+\sqrt{x}+2+\sqrt{x}-2}{\left(\sqrt{x}-2\right)\left(\sqrt{x}+2\right)}\)

\(N=\frac{x+2\sqrt{x}}{\left(\sqrt{x}-2\right)\left(\sqrt{x}+2\right)}\)

\(N=\frac{\left(\sqrt{x}+2\right)\sqrt{x}}{\left(\sqrt{x}-2\right)\left(\sqrt{x}+2\right)}\)

\(N=\frac{\sqrt{x}}{\sqrt{x}-2}\)

b) \(N=-\frac{1}{3}\)

\(\Leftrightarrow\frac{\sqrt{x}}{\sqrt{x}-2}=-\frac{1}{3}\)

\(\Leftrightarrow3\sqrt{x}=2-\sqrt{x}\)

\(\Leftrightarrow4\sqrt{x}=2\)

\(\Leftrightarrow\sqrt{x}=\frac{1}{2}\Rightarrow x=\frac{1}{4}\)

c) \(N=\frac{\sqrt{25}}{\sqrt{25}-2}=\frac{5}{5-2}=\frac{5}{3}\)