#### Answer

a| b means that for some integer m, b = am
a ∤c means that for some integer n, c = an + x where x is any integer such that x is not divisible by a
Then,
(b + c)/a = (am + an + x)/a = (a(m + n)+x)/a
= a(m + n)/a+ x/a = (m+n)+ x/a
Since x/a is not an integer, we conclude that a ∤ (b+c) if a| b and a ∤c

#### Work Step by Step

Steps:
1. Express b in terms of a by division rule (if a| b then b = am for some integer m)
2. Express c in terms of a.
3. Compute \frac{b+c}{a} by putting the value of b and c from step 1 and step 2.