Find all integers `n` for which (n^2+13n+2)/(3n+5) also an Integer ?

And Please give me some hint that How to slove such type of Questions ?

Dear student,

Here goes the hint:

6n² + 13n + 6 = 0
n² + 13/12n = - 1 + (13/12)²
n² + 13/12n = - 144/144 + 169/144
(n - 13/12)² = 25/144
n - 13/12 = ± 5/12

n = 5/12 + 13/12, n = 18/12, n = 3/2
n = - 5/12 + 13/12, n = 8/12, n = 2/3

Answer: n = 3/2, 2/3

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