7. For which integers n is the value of the fraction $\frac{n^{2}+2 n-8}{n^{2}-4}$ an integer?
7. It holds that $\frac{n^{2}+2 n-8}{n^{2}-4}=\frac{n+4}{n+2}$.

3 POINTS

Further, $\frac{n+4}{n+2}=\frac{n+2+2}{n+2}=\frac{n+2}{n+2}+\frac{2}{n+2}=1+\frac{2}{n+2}$.

3 POINTS

The given fraction will be an integer only if $n+2$ is a divisor of the number 2, that is, if $n+2 \in \{1, -1, 2, -2\}$.

2 POINTS

or if $n \in \{-1, -3, 0, -4\}$.

2 POINTS

TOTAL 10 POINTS