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

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

A= \(\left(\frac{1}{1+\sqrt{x}}\right):\left(\frac{x-9}{\left(\sqrt{x}-2\right)\left(\sqrt{x}-3\right)}-\frac{x-4}{\left(\sqrt{x}-3\right)\left(\sqrt{x}-2\right)}+\frac{\sqrt{x}+2}{\left(\sqrt{x}-2\right)\left(\sqrt{x}-3\right)}\right)\)

A=\(\left(\frac{1}{1+\sqrt{x}}\right):\left(\frac{x-9-x+4+\sqrt{x}+2}{\left(\sqrt{x}-2\right)\left(\sqrt{x}-3\right)}\right)\)

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

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

bạn rút gọc câu a chưa

b) Để A = \(\frac{1}{2}\)

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

=> 2\(\sqrt{x}-4\)=\(\sqrt{x}+1\)

=> \(\sqrt{x}=5\)

=> x = 25

a: \(A=\dfrac{1}{\sqrt{x}+1}:\left(\dfrac{x-9-x+4+\sqrt{x}+2}{\left(\sqrt{x}-2\right)\left(\sqrt{x}-3\right)}\right)\)

\(=\dfrac{1}{\sqrt{x}+1}\cdot\dfrac{\left(\sqrt{x}-2\right)\left(\sqrt{x}-3\right)}{\sqrt{x}-3}\)

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

b: Để A<0 thì \(\sqrt{x}-2< 0\)

hay 0<x<4

\(A=\frac{2\sqrt{x}+1}{x+\sqrt{x}+1}\)với \(x=16\Rightarrow\sqrt{x}=4\)

\(=\frac{2.4+1}{16+4+1}=\frac{9}{21}=\frac{3}{7}\)

Vậy với x = 16 thì A nhận giá trị là 3/7 

b, Sửa rút gọn biểu thức B nhé 

Với \(x\ge0;x\ne1\)

\(B=\left(\frac{1}{\sqrt{x}-1}-\frac{\sqrt{x}}{1-x}\right):\left(\frac{\sqrt{x}}{\sqrt{x}-1}-1\right)\)

\(=\left(\frac{1}{\sqrt{x}-1}+\frac{\sqrt{x}}{\left(\sqrt{x}\pm1\right)}\right):\left(\frac{\sqrt{x}-\sqrt{x}+1}{\sqrt{x}-1}\right)\)

\(=\frac{\sqrt{x}+1+\sqrt{x}}{\left(\sqrt{x}\pm1\right)}.\frac{\sqrt{x}-1}{1}=\frac{2\sqrt{x}}{\sqrt{x}+1}\)

c, Ta có : \(M=\frac{A}{B}\)hay \(M=\frac{\frac{2\sqrt{x}+1}{x+\sqrt{x}+1}}{\frac{2\sqrt{x}}{\sqrt{x}+1}}\)

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

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

\(ĐKXĐ:x\ge0;x\ne1\)

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

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

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

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

là \(\frac{1}{2\sqrt{x}-2}-\frac{1}{2\sqrt{x}+2}+\frac{\sqrt{x}}{1-x}nha toi bi nham\)

a( \(P=\frac{x-3}{\sqrt{x-1}-\sqrt{2}}\)(ĐKXĐ : \(1\le x\ne3\))

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

b) \(x=4\left(2-\sqrt{3}\right)\Rightarrow x-1=7-4\sqrt{3}=\left(2-\sqrt{3}\right)^2\)

Thay vào P được : \(P=2-\sqrt{3}+\sqrt{2}\)

c) Với mọi \(x\ge1,x\ne3\)ta luôn có \(\sqrt{x-1}\ge0\Rightarrow\) \(P=\sqrt{x-1}+\sqrt{2}\ge\sqrt{2}\). Dấu "=" xảy ra khi x = 1

Vậy Min P = \(\sqrt{2}\Leftrightarrow x=1\)

2. a) \(Q=\frac{\sqrt{x+2}-1}{x+1}\)(ĐKXĐ: \(-2\le x\ne-1\))

\(=\frac{\left(\sqrt{x+2}-1\right)\left(\sqrt{x+2}+1\right)}{\left(x+1\right)\left(\sqrt{x+2}+1\right)}=\frac{x+2-1}{\left(x+1\right)\left(\sqrt{x+2}+1\right)}=\frac{x+1}{\left(x+1\right)\left(\sqrt{x+2}+1\right)}=\frac{1}{\sqrt{x+2}+1}\)b) \(x=40,25=\frac{161}{4}\Rightarrow x+2=\frac{169}{4}\Rightarrow Q=\frac{1}{\sqrt{\frac{169}{4}}+1}=\frac{1}{\frac{13}{2}+1}=\frac{2}{15}\)

c)  Ta có : \(Max_Q\Leftrightarrow Min_{\left(\sqrt{x+2}+1\right)}\) 

Mà : \(\sqrt{x+2}+1\ge1\) với mọi \(-2\le x\ne-1\)

Do đó Max Q = 1 \(\Leftrightarrow x=-2\)