Polynomial Reciprocal on Integers

Algebra Level 3

\( f(x) \) is a degree 4 polynomial satisfying \( f(n) = \frac {1} {n} \) for integers \( n = \) 1 to 5. If \( f(0) = \frac {a} {b} \), where \( a\) and \(b\) are coprime positive integers. What is the value of \( a + b\)?

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