a.
ĐKXĐ: \(x\ne\left\{0;1;-1\right\}\)
\(A=\left[\dfrac{2}{3x}-\dfrac{2}{x+1}.\left(\dfrac{x+1}{3x}-\left(x+1\right)\right)\right]:\dfrac{x-1}{x}\)
\(=\left[\dfrac{2}{3x}-\dfrac{2}{x+1}.\left(x+1\right).\left(\dfrac{1}{3x}-1\right)\right]:\dfrac{x-1}{x}\)
\(=\left[\dfrac{2}{3x}-2\left(\dfrac{1}{3x}-1\right)\right]:\dfrac{x-1}{x}\)
\(=\left(\dfrac{2}{3x}-\dfrac{2}{3x}+2\right):\dfrac{x-1}{x}\)
\(=2:\dfrac{x-1}{x}=\dfrac{2x}{x-1}\)
b.
\(A=\dfrac{2x}{x-1}=\dfrac{2x-2+2}{x-1}=2+\dfrac{2}{x-1}\)
A nguyên \(\Leftrightarrow\dfrac{2}{x-1}\in Z\)
\(\Rightarrow x-1\inƯ\left(2\right)=\left\{-2;-1;1;2\right\}\)
\(\Rightarrow x\in\left\{-1;0;2;3\right\}\)
Kết hợp ĐKXĐ \(\Rightarrow x\in\left\{2;3\right\}\)
