a) ĐK: \(x-9\ne0\Leftrightarrow\left(\sqrt{x}-3\right)\left(\sqrt{x}+3\right)\ne0\)

Vì \(\sqrt{x}\ge0\Rightarrow\sqrt{x}+3>0\)

Nên \(\sqrt{x}-3\ne0\Leftrightarrow x\ne9\)

b) \(P=\left[\frac{2\sqrt{x}\left(\sqrt{x}-3\right)+\sqrt{x}\left(\sqrt{x}+3\right)-\left(3x+3\right)}{\left(\sqrt{x}-3\right)\left(\sqrt{x}+3\right)}\right]:\left(\frac{2\sqrt{x}-2-\left(\sqrt{x}-3\right)}{\sqrt{x}-3}\right)\)

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

\(=\left[\frac{-3\sqrt{x}-3}{\left(\sqrt{x}-3\right)\left(\sqrt{x}+3\right)}\right]\left(\frac{\sqrt{x}-3}{\sqrt{x}+1}\right)\)

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

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

c) Ta có: \(\sqrt{x}+3\ge3\)

\(\Rightarrow\frac{3}{\sqrt{x}+3}\le\frac{3}{3}=1\)

\(\Rightarrow\frac{-3}{\sqrt{x}+3}\ge-1\)

Dấu "=" xảy ra khi \(x=0\)

Vậy \(P_{min}=-1\) khi \(x=0\)

d) \(\frac{-3}{\sqrt{x}+3}< \frac{-1}{3}\)

\(\Leftrightarrow-\left(\sqrt{x}+3\right)< -9\)

\(\Leftrightarrow-\sqrt{x}< -6\)

\(\Leftrightarrow\sqrt{x}>6\)

\(\Leftrightarrow x>36\)

e) Thế \(x=3-2\sqrt{2}\) vào P ta được:

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

f) \(P=\frac{-3}{\sqrt{x}+3}=-2\Leftrightarrow\sqrt{x}+3=6\Leftrightarrow\sqrt{x}=3\Leftrightarrow x=9\)

P/s : sửa đề 

ĐKXĐ : \(\hept{\begin{cases}x\ge0\\x\ne9\end{cases}}\)

a) \(P=\left(\frac{2\sqrt{x}}{\sqrt{x}+3}+\frac{\sqrt{x}}{\sqrt{x}-3}-\frac{3x+3}{x-9}\right):\left(\frac{2\sqrt{x}-2}{\sqrt{x}-3}-1\right)\)

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

\(P=\frac{2x-6\sqrt{x}+x+3\sqrt{x}-3x-3}{x-9}.\frac{\sqrt{x}-3}{\sqrt{x}+1}\)

\(P=\frac{-3\sqrt{x}-3x}{x-9}.\frac{\sqrt{x}-3}{\sqrt{x}+1}\)

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

\(P=\frac{-3\sqrt{x}}{\sqrt{x}+3}\)

b) \(P< -\frac{1}{2}\)

\(\Leftrightarrow\frac{-3\sqrt{x}}{\sqrt{x}+3}+\frac{1}{2}< 0\)

\(\Leftrightarrow\frac{-6\sqrt{x}+\sqrt{x}+3}{2\left(\sqrt{x}+3\right)}< 0\)

\(\Leftrightarrow\frac{-5\sqrt{x}+3}{2\left(\sqrt{x}+3\right)}< 0\)

Mà \(2\left(\sqrt{x}+3\right)>0\)

\(\Rightarrow-5\sqrt{x}+3< 0\)

\(\Leftrightarrow-5\sqrt{x}< -3\)

\(\Leftrightarrow\sqrt{x}>\frac{3}{5}\)

\(\Leftrightarrow x>\frac{9}{25}\)

Vấy .................

c) \(P.\left(\sqrt{x}+3\right)+2\sqrt{x}-2+x=2\)

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

\(\Leftrightarrow-3\sqrt{x}+2\sqrt{x}-2-2+x=0\)

\(\Leftrightarrow-\sqrt{x}-4+x=0\)

\(\Leftrightarrow-\sqrt{x}\left(1-\sqrt{x}\right)=4\)

Còn lại lập bảng tự tìm giá trị của x là ra .( Chú ý : đối chiếu ĐKXĐ )

d) 

\(P.\left(\sqrt{x}+3\right)+x\left(\sqrt{x}-m\right)=x-\sqrt{x}\left(3+m\right)\)

\(\Leftrightarrow\frac{-3\sqrt{x}}{\sqrt{x}+3}\left(\sqrt{x}+3\right)+x\sqrt{x}-xm=x-3\sqrt{x}-m\sqrt{x}\)

\(\Leftrightarrow-3\sqrt{x}+x\sqrt{x}-xm-x+3\sqrt{x}+m\sqrt{x}=0\)

\(\Leftrightarrow\sqrt{x}\left(x+m\right)-x\left(m+1\right)=0\)

\(\Leftrightarrow\sqrt{x}\left[x+m-m\sqrt{x}-\sqrt{x}\right]=0\)

\(\Leftrightarrow\sqrt{x}\left[m\left(1-\sqrt{x}\right)-\sqrt{x}\left(1-\sqrt{x}\right)\right]=0\)

\(\Leftrightarrow\sqrt{x}=0;m-\sqrt{x}=0;1-\sqrt{x}=0\)

+) \(\sqrt{x}=0\Leftrightarrow x=0\left(TM\right)\)

+) \(1-\sqrt{x}=0\)

\(\Leftrightarrow x=1\left(TM\right)\)

+) \(m-\sqrt{x}=0\)

\(\Leftrightarrow\orbr{\begin{cases}m-\sqrt{0}=0\\m-\sqrt{1}=0\end{cases}\Leftrightarrow\orbr{\begin{cases}m=0\\m=1\end{cases}}}\)

Vậy ..................

a: \(A=\dfrac{\left(\sqrt{a}-\sqrt{b}\right)^2}{\sqrt{a}-\sqrt{b}}-\dfrac{\sqrt{ab}\left(\sqrt{a}+\sqrt{b}\right)}{\sqrt{ab}}\)

\(=\sqrt{a}-\sqrt{b}-\sqrt{a}-\sqrt{b}=-2\sqrt{b}\)

b: \(B=\dfrac{2\sqrt{x}-x-x-\sqrt{x}-1}{\left(\sqrt{x}-1\right)\left(x+\sqrt{x}+1\right)}\cdot\dfrac{x+\sqrt{x}+1}{x-1}\)

\(=\dfrac{-2x+\sqrt{x}-1}{\sqrt{x}-1}\cdot\dfrac{1}{x-1}\)

c: \(C=\dfrac{x-9-x+3\sqrt{x}}{x-9}:\left(\dfrac{3-\sqrt{x}}{\sqrt{x}-2}+\dfrac{\sqrt{x}-2}{\sqrt{x}+3}+\dfrac{x-9}{x+\sqrt{x}-6}\right)\)

\(=\dfrac{3\left(\sqrt{x}-3\right)}{x-9}:\dfrac{9-x+x-4\sqrt{x}+4+x-9}{\left(\sqrt{x}+3\right)\left(\sqrt{x}-2\right)}\)

\(=\dfrac{3}{\sqrt{x}+3}\cdot\dfrac{\left(\sqrt{x}+3\right)\left(\sqrt{x}-2\right)}{x-4\sqrt{x}+4}\)

\(=\dfrac{3}{\sqrt{x}-2}\)

\(a,x>0;x\ne4,9\)

\(b,Q=\left(\frac{1}{\sqrt{x}-3}-\frac{1}{\sqrt{x}}\right):\left(\frac{\sqrt{x}+3}{\sqrt{x}-2}-\frac{\sqrt{x}+2}{\sqrt{x}-3}\right)\)

\(Q=\left(\frac{\sqrt{x}-\sqrt{x}+3}{x-3\sqrt{x}}\right):\left(\frac{x-9-x+4}{\left(\sqrt{x}-2\right)\left(\sqrt{x}-3\right)}\right)\)

\(Q=\frac{3}{x-3\sqrt{x}}:\frac{-5}{\left(\sqrt{x}-2\right)\left(\sqrt{x}-3\right)}\)

\(Q=\frac{3}{\sqrt{x}\left(\sqrt{x}-3\right)}.\frac{\left(\sqrt{x}-2\right)\left(\sqrt{x}-3\right)}{-5}\)

\(Q=\frac{3\sqrt{x}-6}{-5\sqrt{x}}\)

\(c,Q< 0< =>\frac{3\sqrt{x}-6}{-5\sqrt{x}}\)

\(-5\sqrt{x}< 0\)

\(< =>3\sqrt{x}-6>0\)

\(\sqrt{x}>2\)

\(x>4\)

a) ĐKXĐ:  \(x\ge0;x\ne9\)

mk chỉnh lại đề bài nhé, chắc có lẽ bn ghi nhầm:

\(P=\left(\frac{2\sqrt{x}}{\sqrt{x}+3}+\frac{\sqrt{x}}{\sqrt{x}-3}-\frac{3x+3}{x-9}\right):\left(\frac{2\sqrt{x}-2}{\sqrt{x}-3}-1\right)\)

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

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

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

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

\(a,P=\left(1-\frac{x-3\sqrt{x}}{x-9}\right):\left(\frac{9-x}{x+\sqrt{x}-6}-\frac{\sqrt{x}-3}{2-\sqrt{x}}-\frac{\sqrt{x}-2}{\sqrt{x}+3}\right)\)\(ĐKXĐ:\hept{\begin{cases}x\ge0\\x\ne4\\x\ne9\end{cases}}\)

       \(=\left(1-\frac{\sqrt{x}\left(\sqrt{x}-3\right)}{\left(\sqrt{x}-3\right)\left(\sqrt{x}+3\right)}\right):\left(\frac{\left(3-\sqrt{x}\right)\left(3+\sqrt{x}\right)}{\left(\sqrt{x}-2\right)\left(\sqrt{x}+3\right)}+\frac{\sqrt{x}-3}{\sqrt{x}-2}-\frac{\sqrt{x}-2}{\sqrt{x}+3}\right)\)

       \(=\left(1-\frac{\sqrt{x}}{\sqrt{x}+3}\right):\left(\frac{3-\sqrt{x}}{\sqrt{x}-2}+\frac{\sqrt{x}-3}{\sqrt{x}-2}-\frac{\sqrt{x}-2}{\sqrt{x}+3}\right)\)

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

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

       \(=\frac{3}{2-\sqrt{x}}\)

b, Để P > 0 thì \(2-\sqrt{x}>0\Leftrightarrow\sqrt{x}< 2\Leftrightarrow0\le x< 4\)(Thỏa mãn DKXD)

\(c,Q=P\left(x+1\right)=\frac{3\left(x+1\right)}{2-\sqrt{x}}\)

Ko biết e đã học miền giá trị chưa nhỉ ???

\(a)\)\(R=\left(\frac{2\sqrt{x}}{\sqrt{x}+3}+\frac{\sqrt{x}}{\sqrt{x}-3}-\frac{3\left(\sqrt{x}+3\right)}{x-9}\right):\left(\frac{2\sqrt{x}-2}{\sqrt{x}-3}-1\right)\)

\(R=\left(\frac{2\sqrt{x}}{\sqrt{x}+3}+\frac{\sqrt{x}}{\sqrt{x}-3}-\frac{3\left(\sqrt{x}+3\right)}{\left(\sqrt{x}-3\right)\left(\sqrt{x}+3\right)}\right):\frac{\sqrt{x}+1}{\sqrt{x}-3}\)

\(R=\left(\frac{2\sqrt{x}}{\sqrt{x}+3}+\frac{\sqrt{x}}{\sqrt{x}-3}-\frac{3}{\sqrt{x-3}}\right):\frac{\sqrt{x}+1}{\sqrt{x}-3}\)

\(R=\left(\frac{2\sqrt{x}}{\sqrt{x}+3}+\frac{\sqrt{x}-3}{\sqrt{x}-3}\right):\frac{\sqrt{x}+1}{\sqrt{x}-3}\)

\(R=\left(\frac{2\sqrt{x}}{\sqrt{x}+3}+1\right):\frac{\sqrt{x}+1}{\sqrt{x}-3}\)

\(R=\frac{3\sqrt{x}+3}{\sqrt{x}+3}.\frac{\sqrt{x}-3}{\sqrt{x+1}}\)

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

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

\(b)\) Ta có : \(R< -1\)

\(\Leftrightarrow\)\(\frac{3\left(\sqrt{x}-3\right)}{\sqrt{x}+3}< -1\)

\(\Leftrightarrow\)\(\frac{\sqrt{x}-3}{\sqrt{x}+3}< \frac{-1}{3}\)

\(\Leftrightarrow\)\(3\sqrt{x}-9< -\sqrt{x}-3\)

\(\Leftrightarrow\)\(4\sqrt{x}< 6\)

\(\Leftrightarrow\)\(\sqrt{x}< \frac{3}{2}\)

\(\Leftrightarrow\)\(x< \frac{9}{4}\)

Chúc bạn học tốt ~