若A、B为有理数,且满足 3x+4\（x-2)(x+3) = A\x-2 - B\x+3,求A、B的值

通分：(3x+4)/(x-2)(x+3) = A(x+3)/(x-2)(x+3) - B(x-2)/(x-2)(x+3)
即：3x+4 = A(x+3) - B(x-2)
3x+4 = Ax + 3A - BX + 2B
3x+4 = (A-B)x + (3A+2B)
则有：A-B=3.①
3A+2B=4.②
①×2 + ②,得：5A=10
A=2
则B=-1