Question

câu 1: Rút gọn: \(A=\frac{x\left|x-2\right|}{x^2+8x-20}\)

câu 2: tìm x biết:

a) |2x - 3| > 5

b) |3x - 1| \(\le7\)

c) |3x - 5| + |2x + 3| = 7

Answer 1

\(A=\frac{x\left|x-2\right|}{x^2+8x-20}=\frac{x\left|x-2\right|}{x^2-2x+10x-20}=\frac{x\left|x-2\right|}{x\left(x-2\right)+10\left(x-2\right)}=\frac{x\left|x-2\right|}{\left(x+10\right)\left(x-2\right)}\)

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 :

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