a: ĐKXĐ: \(x\notin\left\{2;-2;3\right\}\)
\(A=\left(\dfrac{-\left(x+2\right)}{x-2}+\dfrac{x-2}{x+2}-\dfrac{4x^2}{\left(x-2\right)\left(x+2\right)}\right):\dfrac{\left(x-3\right)^2}{\left(2-x\right)\left(x-3\right)}\)
\(=\dfrac{-x^2-4x-4+x^2-4x+4-4x^2}{\left(x-2\right)\left(x+2\right)}\cdot\dfrac{-\left(x-2\right)}{x-3}\)
\(=\dfrac{-4x^2-8x}{x+2}\cdot\dfrac{-1}{x-3}=\dfrac{4x}{x-3}\)
b: |x|=1/3 nên x=1/3 hoặc x=-1/3
Khi x=1/3 thì \(A=\dfrac{\dfrac{4}{3}}{\dfrac{1}{3}-3}=\dfrac{4}{3}:\dfrac{-8}{3}=\dfrac{-1}{2}\)
Khi x=-1/3 thì \(A=\dfrac{-\dfrac{4}{3}}{-\dfrac{1}{3}-3}=\dfrac{-4}{3}:\dfrac{-10}{3}=\dfrac{2}{5}\)
c: Để A<1 thi A-1<0
=>\(\dfrac{4x-x+3}{x-3}< 0\)
=>(3x+3)/(x-3)<0
=>-1<x<3
