# 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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