a: \(A=\dfrac{1-2x}{\left(x-1\right)\left(x-2\right)}+\dfrac{x+1}{x-2}\)
\(=\dfrac{1-2x+x^2-1}{\left(x-2\right)\left(x-1\right)}=\dfrac{x^2-2x}{\left(x-2\right)\left(x-1\right)}=\dfrac{x}{x-1}\)
\(B=\dfrac{2x^2+2x}{1-x^2}=\dfrac{2x\left(x+1\right)}{\left(1-x\right)\left(1+x\right)}=\dfrac{2x}{1-x}\)
b: \(D=B-A=\dfrac{-2x}{x-1}-\dfrac{x}{x-1}=\dfrac{-3x}{x-1}\)
c: Để D là số nguyên thì \(-3x+3-3⋮x-1\)
\(\Leftrightarrow x-1\in\left\{1;-1;3;-3\right\}\)
hay \(x\in\left\{0;4;-2\right\}\)
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