Question

Rút gọn biểu thức \(\frac{x|x-2|}{x^2+8x-20}+12x-3\)

Answer 1

\(A=\)\(\frac{x|x-2|}{x^2+8x-20}+12x-3.\)

\(=\frac{x|x-2|}{\left(x-2\right)\left(x+10\right)}+12x-3\)

Nếu \(x\ge2\Rightarrow x-2\ge0\Leftrightarrow|x-2|=x-2\)

\(\Rightarrow A=\frac{x\left(x-2\right)}{\left(x-2\right)\left(x+10\right)}+12x-3=\frac{x}{x+10}+12x-3\)

Nếu \(x< 2\Rightarrow x-2< 0\Leftrightarrow|x-2|=-\left(x-2\right)\)

\(\Rightarrow A=\frac{-x\left(x-2\right)}{\left(x-2\right)\left(x+10\right)}+12x-3=\frac{-x}{x+10}+12x-3\)

Answer 2

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