a: \(A=\left(\frac{x-4}{x}-\frac{x}{x-4}+\frac{16}{x^2-4x}\right)\cdot\frac{x}{2x-2}\)
\(=\frac{\left(x-4\right)^2-x^2+16}{x\left(x-4\right)}\cdot\frac{x}{2\left(x-1\right)}\)
\(=\frac{x^2-8x+16-x^2+16}{x\left(x-4\right)}\cdot\frac{x}{2\left(x-1\right)}=\frac{-8x+32}{\left(x-4\right)\cdot2\cdot\left(x-1\right)}\)
\(=\frac{-8\left(x-4\right)}{2\left(x-4\right)\left(x-1\right)}=\frac{-4}{x-1}\)
b: |x+2|=6
=>x+2=6 hoặc x+2=-6
=>x=4(loại) hoặc x=-8(nhận)
Thay x=-8 vào A, ta được:
\(A=\frac{-4}{-8-1}=\frac{-4}{-9}=\frac49\)
c: A nguyên
=>-4⋮x-1
=>x-1∈{1;-1;2;-2;4;-4}
=>x∈{2;0;3;-1;5;-3}
Kết hợp ĐKXĐ, ta được: x∈{2;3;-1;5;-3}
