Sửa đề: \(M=\left(\dfrac{x+1}{x-1}-\dfrac{x^2-x}{x^2+x}\right):\dfrac{x}{2x+2}\)
a: ĐKXĐ: x<>0; x<>1; x<>-1
b: \(M=\left(\dfrac{x+1}{x-1}-\dfrac{x\left(x-1\right)}{x\left(x+1\right)}\right):\dfrac{x}{2\left(x+1\right)}\)
\(=\left(\dfrac{x+1}{x-1}-\dfrac{x-1}{x+1}\right):\dfrac{x}{2\left(x+1\right)}\)
\(=\dfrac{x^2+2x+1-x^2+2x-1}{\left(x-1\right)\left(x+1\right)}:\dfrac{x}{2\left(x+1\right)}\)
\(=\dfrac{4x}{\left(x-1\right)\left(x+1\right)}\cdot\dfrac{2\left(x+1\right)}{x}\)
\(=\dfrac{8x\left(x+1\right)}{x\left(x-1\right)\left(x+1\right)}=\dfrac{8}{x-1}\)
c: M=1
=>x-1=8
=>x=9(nhận)
d: M<0
=>x-1<0
=>x<1
e: M nguyên
=>x-1 thuộc {1;-1;2;-2;4;-4;8;-8}
=>x thuộc {3;-1;5;-3;9;-7}
