a) ĐKXĐ: \(x\ne1,x\ne-1,x\ne0\)
b) \(P=\left(\dfrac{x+1}{x-1}-\dfrac{x-1}{x+1}\right):\dfrac{2x}{5x-5}-\dfrac{x^2-1}{x^2+2x+1}=\dfrac{\left(x+1\right)^2-\left(x-1\right)^2}{\left(x-1\right)\left(x+1\right)}.\dfrac{5\left(x-1\right)}{2x}-\dfrac{\left(x-1\right)\left(x+1\right)}{\left(x+1\right)^2}=\dfrac{20x}{2x\left(x+1\right)}-\dfrac{x-1}{x+1}=\dfrac{10}{x+1}-\dfrac{x-1}{x+1}=\dfrac{10-x+1}{x+1}=\dfrac{11-x}{x+1}\)
c) \(P=\dfrac{11-x}{x+1}=2\Leftrightarrow2x+2=11-x\Leftrightarrow3x=9\Leftrightarrow x=3\)
d) \(P=\dfrac{11-x}{x+1}=\dfrac{-\left(x+1\right)}{x+1}+\dfrac{12}{x+1}=-1+\dfrac{12}{x+1}\in Z\)
\(\Rightarrow x+1\inƯ\left(12\right)=\left\{1;-1;2;-2;3;-3;4;-4;6;-6;12;-12\right\}\)
Do \(x\ne1,x\ne-1,x\ne0\)
\(\Rightarrow x\in\left\{-2;-3;2;-4;3;-5;5;-7;11;-13\right\}\)
a: ĐKXĐ: \(x\notin\left\{1;-1;0\right\}\)
b: Ta có: \(P=\left(\dfrac{x+1}{x-1}-\dfrac{x-1}{x+1}\right):\dfrac{2x}{5x-5}-\dfrac{x^2-1}{x^2+2x+1}\)
\(=\dfrac{x^2+2x+1-x^2+2x-1}{\left(x-1\right)\left(x+1\right)}\cdot\dfrac{5\left(x-1\right)}{2x}-\dfrac{x-1}{x+1}\)
\(=\dfrac{2}{x+1}-\dfrac{x-1}{x+1}\)
\(=\dfrac{2-x+1}{x+1}\)
\(=\dfrac{3-x}{x+1}\)
c: Để P=2 thì \(3-x=2x+2\)
\(\Leftrightarrow-3x=-1\)
hay \(x=\dfrac{1}{3}\)
d: Để P là số nguyên thì \(x-3⋮x+1\)
\(\Leftrightarrow x+1\in\left\{-1;1;2;-2;4;-4\right\}\)
hay \(x\in\left\{-2;0;-3;3;-5\right\}\)
