To find the overall remainder in a Remainders and Addition problem, find the remainder of each term separately and then add them together. For example, what is the remainder of the following problem below:
$$\frac{17+9}{5}$$
This remainder is equal to the remainder of each term added together:
$$\frac{17}{5} + \frac{9}{5} = 2 \ (remainder) + 4 \ (remainder) = 6$$
If the resulting remainder sum is less than $5$ in this case, say $0$, $1$, $2$, $3$, or $4$, then that's simply the remainder because all of those values are less than $5$. If however, the remainder sum is equal to or greater than the divisor, then the final remainder is equal to the remainder sum minus $5$:
$$6-5=1 = \ final \ remainder$$
Of course you wouldn't solve this problem this way because it's so obvious that $(17+9) \div 5$ has a remainder of $1$, but you could use this trick in a problem like the one below that asks you to find the remainder:
$$\frac{7^{30}+6^{45}}{3}$$