Question

Answer 1

a) \(A=\left(\dfrac{1}{1-x}+\dfrac{2}{x+1}-\dfrac{5-x}{1-x^2}\right):\dfrac{1-2x}{x^2-1}\)

\(A=\left(\dfrac{x+1-2x+2-5+x}{1-x^2}\right):\dfrac{2x-1}{1-x^2}=\left(\dfrac{-2}{1-x^2}\right).\dfrac{1-x^2}{2x-1}=\dfrac{2}{1-2x}\)

b) \(A=\dfrac{2}{1-2x}\in Z\Rightarrow1-2x\in U\left(2\right)=\left\{-1;1;-2;2\right\}\)

\(\Rightarrow x\in\left\{1;0\right\}\)

c) \(\left|\dfrac{2}{1-2x}\right|=\dfrac{2}{1-2x}\)

\(\Rightarrow\dfrac{2}{1-2x}\ge0\Rightarrow1-2x\ge0\Rightarrow x\le\dfrac{1}{2}\)

Answer 2

Sửa lại x<1/2