Biết \(\frac{6x^{2}+17x-5}{(x+1)(x+2)(x+3)}=\frac{a}{x+1}+\frac{b}{x+2}+\frac{c}{x-3}\), \(\forall x\notin \{-1;-2;3\}\). Tính \(a+b+c\)

Bài 6. Biết \(\frac{6x^{2}+17x-5}{(x+1)(x+2)(x+3)}=\frac{a}{x+1}+\frac{b}{x+2}+\frac{c}{x-3}\), \(\forall x\notin \{-1;-2;3\}\). Tính \(a+b+c\).