Question

Cho A= 1 - \(\dfrac{1}{x+2}\) , Tìm x nguyên để  A nguyên

Answer 1

Để A là số nguyên thì 1 chia hết cho x+2

=>\(x+2\in\left\{1;-1\right\}\)

hay \(x\in\left\{-1;-3\right\}\)

Answer 2

Để A ∈Z <=> \(\dfrac{1}{x+2}\in Z\Leftrightarrow\left(x+2\right)\in U\left(1\right)=\pm1\)

<=>\(\left[{}\begin{matrix}x+2=1\\x+2=-1\end{matrix}\right.< =>\left[{}\begin{matrix}x=-1\\x=-3\end{matrix}\right.\)