7:
a: ĐKXĐ: x<>0; x<>2; x<>-2
\(A=\left(\dfrac{x}{\left(x-2\right)\left(x+2\right)}-\dfrac{2}{x-2}+\dfrac{1}{x+2}\right):\dfrac{x^2-4+10-x^2}{x+2}\)
\(=\dfrac{x-2\left(x+2\right)+x-2}{\left(x-2\right)\left(x+2\right)}\cdot\dfrac{x+2}{6}\)
\(=\dfrac{2x-2-2x-4}{x-2}\cdot\dfrac{1}{6}=\dfrac{-1}{x-2}\)
b: |x-2|=4
=>x-2=-4 hoặc x-2=4
=>x=6(nhận) hoặc x=-2(loại)
Khi x=6 thì \(A=\dfrac{-1}{6-2}=-\dfrac{1}{4}\)
c: A=2
=>x-2=-1/2
=>x=3/2(nhận)
d: A<0
=>x-2>0
=>x>2
e: A nguyên
=>x-2 thuộc {1;-1}
=>x thuộc {1;3}