\(A=\left(\dfrac{1}{x^2-4x}+\dfrac{2}{16-x^2}+\dfrac{4}{4x+16}\right):\dfrac{1}{4x}\left(x\ne4;x\ne-4;x\ne0\right).\)

\(A=\left(\dfrac{1}{x\left(x-4\right)}+\dfrac{-2}{\left(x+4\right)\left(x-4\right)}+\dfrac{1}{x+4}\right).4x\).

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

\(A=\dfrac{x^2-5x+4}{\left(x-4\right)\left(x+4\right)}.4.\)

\(A=\dfrac{\left(x-4\right)\left(x-1\right)}{\left(x-4\right)\left(x+4\right)}.4.\)

\(A=\dfrac{4\left(x-1\right)}{x+4}.\)

chịch ko em

\(=\left(\dfrac{x-y}{2y-x}-\dfrac{x^2+y^2+y-2}{x^2-2xy+xy-2y^2}\right):\dfrac{\left(2x^2+y\right)^2-4}{x\left(x+y\right)+\left(x+y\right)}:\dfrac{x+y}{2x^2+y+2}\)

\(=\left(\dfrac{x-y}{2y-x}-\dfrac{x^2+y^2+y-2}{\left(x-2y\right)\left(x+y\right)}\right)\cdot\dfrac{\left(x+y\right)\left(x+1\right)}{\left(2x^2+y+2\right)\left(2x^2+y-2\right)}\cdot\dfrac{2x^2+y+2}{x+y}\)

\(=\dfrac{y^2-x^2-x^2-y^2-y+2}{\left(x-2y\right)\left(x+y\right)}\cdot\dfrac{x+1}{2x^2+y-2}\)

\(=\dfrac{-\left(2x^2+y-2\right)}{\left(x-2y\right)\left(x+y\right)}\cdot\dfrac{x+1}{2x^2+y-2}=\dfrac{-\left(x+1\right)}{\left(x-2y\right)\left(x+y\right)}\)

\(A=\frac{4x}{x^2-2x}+\frac{3}{2-x}+\frac{12x}{x^3-4x}\)

\(A=\frac{4x}{x\left(x-2\right)}-\frac{3}{x-2}+\frac{12x}{x\left(x-2\right)\left(x+2\right)}\)

\(A=\frac{4x\left(x+2\right)-3x\left(x+2\right)+12x}{x\left(x-2\right)\left(x+2\right)}\)

\(A=\frac{x\left(x+2\right)+12x}{x\left(x-2\right)\left(x+2\right)}\)

\(A=\frac{x^2+2x+12x}{x\left(x-2\right)\left(x+2\right)}\)

\(A=\frac{x^2+14x}{x\left(x-2\right)\left(x+2\right)}\)

Điều kiện: x\(\ne\) 0; x \(\ne\) 2; -2; 3

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

A = \(\left(\frac{\left(2+x\right)^2}{\left(2-x\right)\left(2+x\right)}+\frac{4x^2}{\left(2-x\right)\left(2+x\right)}-\frac{\left(2-x\right)^2}{\left(2-x\right)\left(2+x\right)}\right).\frac{x\left(2-x\right)}{\left(x-3\right)}\)

A = \(\frac{x^2+4x+4+4x^2-\left(4-4x+x^2\right)}{\left(2-x\right)\left(2+x\right)}.\frac{x\left(2-x\right)}{\left(x-3\right)}\)

A = \(\frac{8x+4x^2}{\left(2+x\right)}.\frac{x}{\left(x-3\right)}=\frac{4x\left(x+2\right)}{\left(x+2\right)}.\frac{x}{x-3}=\frac{4x^2}{x-3}\)

ĐK: \(\hept{\begin{cases}x^2+4x+4\ne0\\4-x^2\ne0\end{cases}}\Rightarrow\hept{\begin{cases}\left(x+2\right)^2\ne0\\\left(2-x\right)\left(2+x\right)\ne0\end{cases}\Rightarrow\hept{\begin{cases}x\ne-2\\x\ne2\end{cases}}}\)

\(P=\frac{x^3-4x}{x^2+4}.\left(\frac{1}{x^2+4x+4}+\frac{1}{4-x^2}\right)\)

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

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

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

Đề sai ạ ! Sửa nhé :

\(S=\left(\frac{2+x}{2-x}+\frac{4x^2}{x^2-4}-\frac{2-x}{2+x}\right):\frac{x^3-4x}{2x^2-x^3}\)

\(\Leftrightarrow S=\left(\frac{-\left(x+2\right)}{x-2}+\frac{4x^2}{\left(x-2\right)\left(x+2\right)}+\frac{x-2}{x+2}\right):\frac{x\left(x^2-4\right)}{x^2\left(2-x\right)}\)

\(\Leftrightarrow S=\left(\frac{-\left(x+2\right)^2+4x^2+\left(x-2\right)^2}{\left(x-2\right)\left(x+2\right)}\right):\frac{\left(x-2\right)\left(x+2\right)}{-x\left(x-2\right)}\)

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

\(\Leftrightarrow S=\frac{-x\left(4x^2-8x\right)}{\left(x+2\right)^2\left(x-2\right)}\)

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

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

P/s : nếu làm theo đề của bạn, sẽ ra kq dài... Nên mik tiện sửa, còn nếu đề bạn đúng rồi thì mik sẽ làm lại ạ !

mình nhầm tí nhé bạn

\(\frac{x^2-3x}{2x^2-x^3}\)

P/s : Làm theo đề đã sửa ạ !

\(S=\left(\frac{2+x}{2-x}+\frac{4x^2}{x^2-4}-\frac{2-x}{2+x}\right):\frac{x^2-3x}{2x^2-x^3}\)

\(\Leftrightarrow S=\left(\frac{-\left(x+2\right)}{x-2}+\frac{4x^2}{\left(x-2\right)\left(x+2\right)}+\frac{x-2}{2+x}\right):\frac{x\left(x-3\right)}{-x^2\left(x-2\right)}\)

\(\Leftrightarrow S=\frac{-\left(x+2\right)^2+4x^2+\left(x-2\right)^2}{\left(x-2\right)\left(x+2\right)}.\frac{-x\left(x-2\right)}{\left(x-3\right)}\)

\(\Leftrightarrow S=\frac{-x\left(-x^2-4x-4+4x^2+x^2-4x+4\right)\left(x-2\right)}{\left(x-2\right)\left(x+2\right)\left(x-3\right)}.\)

\(\Leftrightarrow S=\frac{-x\left(4x^2-8x\right)}{\left(x+2\right)\left(x-3\right)}\)

\(\Leftrightarrow S=\frac{4x^2\left(2-x\right)}{\left(x+2\right)\left(x-3\right)}\)

a) \(ĐKXĐ:\hept{\begin{cases}x\ne0\\x\ne-1\end{cases}}\)

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

\(=\left[\frac{\left(x+2\right)\left(x+1\right)}{3x\left(x+1\right)}+\frac{6x}{3x\left(x+1\right)}-\frac{9x\left(x+1\right)}{3x\left(x+1\right)}\right].\frac{x+1}{2-4x}+\frac{x^2-3x-1}{3x}\)

\(=\left[\frac{x^2+3x+2}{3x\left(x+1\right)}+\frac{6x}{3x\left(x+1\right)}-\frac{9x^2+9x}{3x\left(x+1\right)}\right].\frac{x+1}{2-4x}+\frac{x^2-3x-1}{3x}\)

\(=\frac{x^2+3x+2+6x-9x^2-9x}{3x\left(x+1\right)}.\frac{x+1}{2-4x}+\frac{x^2-3x-1}{3x}\)

\(=\frac{2-8x^2}{3x}.\frac{1}{2\left(1-2x\right)}+\frac{x^2-3x-1}{3x}\)

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

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

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

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

b) Với \(x=6013\)( thỏa mãn ĐKXĐ )

Thay \(x=6013\)vào biểu thức ta được: 

\(M=\frac{6013-1}{3}=\frac{6012}{3}=2004\)

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