ĐKXĐ: `x != 1`

Để `M(x)` nguyên thì `4-x \vdots x-1`

Ta có:

`{(4-x \vdots x-1),(x-1 \vdots x-1):}`

`=> 4-x+x-1 \vdots x-1`

`=> 3 \vdots x-1`

`=> x-1 \in Ư(3) = {+- 1; +-3}`

Ta có bảng sau:

\begin{array}{|c|c|c|}\hline \text{x-1}&\text{1}&\text{-1}&\text{3}&\text{-3}\\\hline \text{x}&\text{2 (TM)}&\text{0 (TM)}&\text{4 (TM)}&\text{-2 (TM)}\\\hline\end{array}

Mà `x<4 => x \in {-2; 0; 2}`

Vậy `x \in {-2; 0; 2}`