a: ĐKXĐ: \(x\notin\left\{2;-2\right\}\)
\(A=\dfrac{x}{2x-4}-\dfrac{x-2}{2x+4}+\dfrac{8}{x^2-4}\)
\(=\dfrac{x}{2\left(x-2\right)}-\dfrac{x-2}{2\left(x+2\right)}+\dfrac{8}{\left(x-2\right)\left(x+2\right)}\)
\(=\dfrac{x\left(x+2\right)-\left(x-2\right)^2+16}{2\left(x-2\right)\left(x+2\right)}\)
\(=\dfrac{x^2+2x-x^2+4x-4+16}{2\left(x-2\right)\left(x+2\right)}\)
\(=\dfrac{6x+12}{2\left(x-2\right)\left(x+2\right)}=\dfrac{6\left(x+2\right)}{2\left(x-2\right)\left(x+2\right)}=\dfrac{3}{x-2}\)
b: Thay x=-4 vào A, ta được:
\(A=\dfrac{3}{-4-2}=\dfrac{3}{-6}=-\dfrac{1}{2}\)
c: Để A là số nguyên thì \(3⋮x-2\)
=>\(x-2\in\left\{1;-1;3;-3\right\}\)
=>\(x\in\left\{3;1;5;-1\right\}\)
