# Rational polynomial

Algebra Level 4

$$f(x)$$ and $$g(x)$$ are monic polynomials with integer coefficients such that

$\frac{f(x)}{g(x)} =\frac{x^3+8}{x^5-2x^4+4x^3}$

and $$\gcd(f(x), g(x) ) = 1$$. What is the value of $$f(4) + g(4)$$?

Details and assumptions

You may use the fact that $$\frac{ f(4) } { g(4) } = \frac{3}{32}$$.

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