n+3 /2n-2 có giá trị nguyên

Để `{n+3}/{2n-2}` có giá trị nguyên

`→n+3\vdots2n-2`

`→2(n+3)\vdots2n-2`

`→2n+6\vdots2n-2`

`→(2n-2)+8\vdots2n-2`

Vì `2n-2\vdots2n-2`

`→(2n-2)+8\vdots2n-2` Khi `8\vdots2n-2`

`→2n-2∈Ư(8)`

`→2n-2∈{±1;±2;±4;±8}`

Ta có bảng:

$$\begin{array}{|c|c|c|}\hline \text{2n-2}&\text{1}&\text{-1}&\text{2}&\text{-2}&\text{4}&\text{-4}&\text{8}&\text{-8}\\\hline \text{n}&\text{1,5}&\text{0,5}&\text{2}&\text{0}&\text{4}&\text{-1}&\text{5}&\text{-3}\\\hline\end{array}$$

Vậy ........