Question
What is the sum of all integer values of n such that 3n+15/(n−1)(n−5) is also an integer
Answers
Steve
since (n-1)(n-5) <= 3n+15 for -1 <= n <= 10, that limits our choices
listing the values of n, (3n+15) and (n-1)(n-5), we have
-1 12 14 no
0 15 5 YES
1 18 0 no
2 21 -3 YES
3 24 -4 YES
4 27 -3 YES
5 30 0 no
6 33 5 no
7 36 12 YES
8 39 21 no
9 42 32 no
10 45 45 YES
0+2+3+4+7+10 = 26
listing the values of n, (3n+15) and (n-1)(n-5), we have
-1 12 14 no
0 15 5 YES
1 18 0 no
2 21 -3 YES
3 24 -4 YES
4 27 -3 YES
5 30 0 no
6 33 5 no
7 36 12 YES
8 39 21 no
9 42 32 no
10 45 45 YES
0+2+3+4+7+10 = 26