Decompose a rational function

Algebra Level 2

Let the rational function \(f\) such that :

\(f(x)=\frac{x^2}{(x-1)(x+2)(x+3)}\)

if the function \(f\) can be written As:

\(\frac{a}{b(x-1)}-\frac{c}{d(x+2)}+\frac{e}{f(x+3)}\)

if \(\frac{a}{b}+\frac{c}{d}+\frac{e}{f}=\frac{m}{n}\)

with \(GCD(m,n)=1\)

Find \(m+n\)

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