Question

Tìm x thuộc Z, biết:
x-6 chia hết cho x+3

Answer 1

\(\Leftrightarrow x+3\in\left\{1;-1;3;-3;9;-9\right\}\)

hay \(x\in\left\{-2;-4;0;-6;6;-12\right\}\)

Answer 2

\(\dfrac{x-6}{x+3}=\dfrac{x+3-6}{x+3}=\dfrac{x+3}{x+3}-\dfrac{6}{x+3}=1-\dfrac{6}{x+3}\)

\(\dfrac{x-6}{x+3}⋮x+3\Rightarrow\dfrac{6}{x+3}⋮x+3\\ \Rightarrow x+3\inƯ_{\left(6\right)}=\left\{-6;-3;-2;-1;1;2;3;6\right\}\)

\(\Rightarrow x\in\left\{-9;-6;-5;-4;-2;-1;0;3\right\}\)