\(a,ĐKXĐ:x\ne0;x\ne1\)

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

\(A=\frac{x^2+x}{\left(x-1\right)^2}:\left[\frac{\left(x+1\right)\left(x-1\right)}{x\left(x-1\right)}+\frac{1}{x\left(x-1\right)}+\frac{2-x^2}{x^2-x}\right]\)

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

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

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

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

a) Đk \(x\ne\pm1\), sau khi rút gọn ta được: (bạn tư làm)

   \(P=\frac{x}{x+1}\)

b) Khi \(\left|x-\frac{2}{3}\right|=\frac{1}{3}\) thì hoặc \(x-\frac{2}{3}=\frac{1}{3}\) hoặc \(x-\frac{2}{3}=-\frac{1}{3}\)

Hay là \(x=1\) hoặc \(x=\frac{1}{3}\)

Do để P có nghĩa thì \(x\ne\pm1\) nên \(x=\frac{1}{3}\), khi đó: 

 \(P=\frac{\frac{1}{3}}{\frac{1}{3}+1}=\frac{1}{4}\)

c) P > 1 khi \(\frac{x}{x+1}>1\)

   \(\Leftrightarrow1-\frac{1}{x+1}>1\)

   \(\Leftrightarrow\frac{1}{x+1}< 0\)

   \(\Leftrightarrow x< -1\)

e) Đề không rõ ràng

dễ mà ko bt lm à

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

<=> M = 

a, Đẻ \(P< 1\)thì : 

\(P=\left(\frac{x}{x+2}+\frac{x}{x-2}-\frac{2}{x^2-4}\right).\frac{x-2}{2x+2}< 1\)

\(=\left(\frac{x\left(x-2\right)\left(x^2-4\right)}{\left(x+2\right)\left(x-2\right)\left(x^2-4\right)}+\frac{x\left(x+2\right)\left(x^2-4\right)}{\left(x-2\right)\left(x+2\right)\left(x^2-4\right)}-\frac{2\left(x+2\right)\left(x-2\right)}{\left(x^2+4\right)\left(x+2\right)\left(x-2\right)}\right).\frac{x-2}{2x+2}\)

\(=\left(\frac{x\left(x-2\right)\left(x^2-4\right)+x\left(x+2\right)\left(x^2-4\right)-2\left(x+2\right)\left(x-2\right)}{\left(x+2\right)\left(x-2\right)\left(x^2-4\right)}\right).\frac{x-2}{2x+2}\)

\(=\left(\frac{2x^4-10x^2+8}{x^4-8x^2+16}\right).\frac{x-2}{2x+2}=\left(2x^4-10x^2+8\right)\left(2x+2\right)=\left(x-2\right)\left(x^4-8x^2+16\right)\)

PT tương đương vs : \(\left(2x^4-10x^2+8\right)\left(2x+2\right)-\left(x-2\right)\left(x^4-8x^2+16\right)< 1\)

Khi đó pt trở thành : \(3x^5+6x^4-12x^3-36x^2+48< 1\)

Chắc vại đó == 

a) \(-ĐKXĐ:x\ne\pm2;1\)

Rút gọn : \(A=\left(\frac{1}{x+2}-\frac{2}{x-2}-\frac{x}{4-x^2}\right):\frac{6\left(x+2\right)}{\left(2-x\right)\left(x+1\right)}\)

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

\(=\left[\frac{x-2}{\left(x-2\right)\left(x+2\right)}+\frac{\left(-2\right)\left(x+2\right)}{\left(x-2\right)\left(x+2\right)}+\frac{x}{\left(x-2\right)\left(x+2\right)}\right]\)\(.\frac{\left(2-x\right)\left(x+1\right)}{6\left(x+2\right)}\)

\(=\left[\frac{x-2-2x-4+x}{\left(x-2\right)\left(x+2\right)}\right].\frac{\left(2-x\right)\left(x+1\right)}{6\left(x+2\right)}\)

\(=\frac{-6}{\left(x-2\right)\left(x+2\right)}.\frac{\left(2-x\right)\left(x+1\right)}{6\left(x+2\right)}\)\(=\frac{x+1}{\left(x+2\right)^2}\)

b) \(A>0\Leftrightarrow\frac{x+1}{\left(x+2\right)^2}>0\Leftrightarrow\orbr{\begin{cases}x+1< 0;\left(x+2\right)^2< 0\left(voly\right)\\x+1>0;\left(x+2\right)^2>0\end{cases}}\)

\(\Leftrightarrow x>1;x>-2\Leftrightarrow x>1\)

Vậy với mọi x thỏa mãn x>1 thì A > 0

c) Ta có : \(x^2+3x+2=0\Leftrightarrow x^2+x+2x+2=0\)

\(\Leftrightarrow x\left(x+1\right)+2\left(x+1\right)=0\Leftrightarrow\left(x+1\right)\left(x+2\right)=0\)

\(\Leftrightarrow\orbr{\begin{cases}x+1=0\\x+2=0\end{cases}}\Leftrightarrow\orbr{\begin{cases}x=-1\\x=-2\end{cases}}\)

Vậy x = -1;-2