chứng minh đẳng thức 2/3x-2/x+1(x+1/3x-x-1) x-1/x=2x/x-1
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![](https://rs.olm.vn/images/avt/0.png?1311)
\(\left[\frac{2}{3x}-\frac{2}{x+1}\left(\frac{x+1}{3x}-x-1\right)\right]:\frac{x-1}{x}\)
\(=\left[\frac{2}{3x}-\frac{2\left(x+1\right)}{\left(x+1\right).3x}-\frac{2\left(-x-1\right)}{x+1}\right]:\frac{x-1}{x}\)
\(=\)\(\left[\frac{2}{3x}-\frac{2\left(x+1\right)}{\left(x+1\right).3x}+\frac{2\left(x+1\right)}{x+1}\right]:\frac{x-1}{x}\)
\(=\left[\frac{2}{3x}-\frac{2}{3x}+2\right]:\frac{x-1}{x}\)
\(=2.\frac{x}{x-1}=\frac{2x}{x-1}\)\(\left(đpcm\right)\)
![](https://rs.olm.vn/images/avt/0.png?1311)
ĐKXĐ:...
\(\left[\frac{2}{3x}-\frac{2}{x+1}\left(\frac{x+1}{3x}-x-1\right)\right]:\frac{x-1}{x}=\left[\frac{2}{3x}-\frac{2}{x+1}\left(\frac{-3x^2-2x+1}{3x}\right)\right]:\frac{x-1}{x}\)
\(=\left[\frac{2}{3x}-\frac{2\left(x+1\right)\left(1-3x\right)}{3x\left(x+1\right)}\right].\frac{x}{x-1}=\left(\frac{2}{3x}-\frac{2\left(1-3x\right)}{3x}\right).\left(\frac{x}{x-1}\right)\)
\(=\left(\frac{2-2+6x}{3x}\right)\left(\frac{x}{x-1}\right)=\frac{2x}{x-1}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(\left[\frac{2}{3x}-\frac{2}{x+1}\left(\frac{x+1}{3x}-x-1\right)\right]:\frac{x-1}{x}=\frac{2x}{x-1}\)( Điều kiện \(x\ne0\))
VT = \(\left[\frac{2}{3x}-\frac{2}{x+1}\left(\frac{x+1}{3x}-x-1\right)\right]:\frac{x-1}{x}\)
\(=\left[\frac{2}{3x}-\frac{2}{x+1}\left(\frac{x+1}{3x}-\frac{3x^2}{3x}-\frac{3x}{3x}\right)\right].\frac{x}{x-1}\)
\(=\left[\frac{2}{3x}-\frac{2}{x+1}\left(\frac{x+1-3x^2-3x}{3x}\right)\right].\frac{x}{x-1}\)
\(=\left(\frac{2}{3x}-\frac{2}{x+1}.\frac{-3x\left(x+1\right)+\left(x+1\right)}{3x}\right).\frac{x}{x-1}\)
\(=\left(\frac{2}{3x}-\frac{2}{x+1}.\frac{\left(x+1\right)\left(-3x+1\right)}{3x}\right).\frac{x}{x-1}\)
\(=\frac{2}{3x}-\frac{2x\left(-3x+1\right)}{3x}.\frac{x}{x-1}\)
\(=\left(\frac{2+6x-2}{3x}\right).\frac{x}{x-1}\)
\(=\frac{6x}{3x}.\frac{x}{x-1}\)
\(=\frac{2x}{x-1}=VP\)
Vậy đẳng thức được chứng minh .
![](https://rs.olm.vn/images/avt/0.png?1311)
a) \(A=\left(3x-2\right)\left(3x+2\right)-\left(3x+1\right)^2-3.\left(-2x-1\right)\)
\(=\left(3x\right)^2-4-\left(9x^2+6x+1\right)+6x+3\)
\(=9x^2-4-9x^2-6x-1+6x+3\)
\(=-2\) không phụ thuộc vào x
b) \(B=\left(x+1\right)\left(x-1\right)-\left(x-2\right)^2-4.\left(x+3\right)\)
\(=x^2-1-\left(x^2-4x+4\right)-\left(4x+12\right)\)
\(=x^2-1-x^2+4x-4-4x-12\)
\(=-17\)không phụ thuộc vào x.
![](https://rs.olm.vn/images/avt/0.png?1311)
ta có \(x\left(x+1\right)\left(x+2\right)=\left(x^2+x\right)\left(x+2\right)\)
\(=x^3+2x^2+x^2+2x\)
\(=x^3+3x^2+2x\)( đpcm )
học tốt
Biến đổi VT ta có :
\(x\left(x+1\right)\left(x+2\right)\)
\(=\left(x^2+x\right)\left(x+2\right)\)
\(=x^3+2x^2+x^2+2x\)
\(=x^3+\left(2x^2+x^2\right)+2x\)
\(=x^3+3x^2+2x=VP\)
Vậy \(x\left(x+1\right)\left(x+2\right)=x^3+3x^2+2x\)
sử dụng thanh công cụ này![](data:image/png;base64,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)
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