B1. Determine all non-zero integers $a$, different from 4, for which the value of the expression $\frac{a}{a-4}+\frac{2}{a}$ is an integer.
B1. If $\frac{a}{a-4}+\frac{2}{a}=\frac{a^{2}+2 a-8}{a(a-4)}$ is an integer, then $a(a-4)$ is a divisor of $a^{2}+2 a-8$. Therefore, $a$ divides $a^{2}+2 a-8$, so $a$ divides 8. All integer divisors of 8, different from 4, are $1, 2, 8, -1, -2, -4$, and -8. We check these seven possibilities and find that the expression is an integer only for $a=2$ and $a=-4$.[^0]