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Ta có: a)(x - 5).(2x +3) - (2x -1).(x +7) - (x -1).(x+2)
= 2x2 + 3x - 10x - 15 - 2x2 - 14x + x + 7 - x2 - 2x + x + 2
= -x2 - 21x - 6
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\(\frac{x+3}{2x-2}-\frac{4}{x^2-1}.\frac{x+1}{2}\)
\(=\frac{x+3}{2x-2}-\left(\frac{4}{x^2-1}.\frac{x+1}{2}\right)\)
\(=\frac{x+3}{2\left(x-1\right)}-\frac{4\left(x+1\right)}{2\left(x-1\right)\left(x+1\right)}\)
\(=\frac{x+3}{2\left(x-1\right)}-\frac{4}{2\left(x-1\right)}\)
\(=\frac{x+3-4}{2\left(x-1\right)}\)
\(=\frac{x-1}{2\left(x-1\right)}\)
\(=\frac{1}{2}\)
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\(A=\frac{x\left|x-2\right|}{x^2+8x-20}=\frac{x\left|x-2\right|}{x^2-2x+10x-20}=\frac{x\left|x-2\right|}{x\left(x-2\right)+10\left(x-2\right)}=\frac{x\left|x-2\right|}{\left(x+10\right)\left(x-2\right)}\)
Xét \(x-2\ge0\Leftrightarrow x\ge2\) ta có :
\(A=\frac{x\left(x-2\right)}{\left(x+10\right)\left(x-2\right)}=\frac{x}{x+10}\)
Xét \(x-2< 0\Leftrightarrow x< 2\) ta có :
\(A=\frac{x\left(2-x\right)}{\left(x+10\right)\left(x-2\right)}=\frac{-x}{x+10}\)
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\(A=\frac{x^2}{x^2-1}-\frac{x^2}{x^2+1}\left(\frac{x}{x+1}+\frac{1}{x^2+x}\right)\)
=>\(A=\frac{x^2}{\left(x-1\right)\left(x+1\right)}-\frac{x^2}{x^2+1}\left[\frac{x}{x+1}+\frac{1}{x\left(x+1\right)}\right]\)
=>\(A=\frac{x^2}{\left(x-1\right)\left(x+1\right)}-\frac{x^2}{x^2+1}\left[\frac{x^2}{x\left(x+1\right)}+\frac{1}{x\left(x+1\right)}\right]\)
=>\(A=\frac{x^2}{\left(x-1\right)\left(x+1\right)}-\frac{x^2}{x^2+1}.\frac{x^2+1}{x\left(x+1\right)}\)
=>\(A=\frac{x^2}{\left(x-1\right)\left(x+1\right)}-\frac{x}{x+1}\)
=>\(A=\frac{x^2}{\left(x-1\right)\left(x+1\right)}-\frac{x\left(x-1\right)}{\left(x+1\right)\left(x-1\right)}\)
=>\(A=\frac{x^2-x\left(x-1\right)}{\left(x-1\right)\left(x+1\right)}\)
=>\(A=\frac{x^2-x^2+x}{\left(x-1\right)\left(x+1\right)}\)
=>\(A=\frac{x}{x^2-1}\)
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\(=\dfrac{x^3-1}{x}\cdot\dfrac{x^2-1+x^2+x+1}{\left(x-1\right)\left(x^2+x+1\right)}=\dfrac{2x^2+x}{x}=2x+1\)