右边通分=[a(x+2)-b(x-3)]/(x-3)(x+2)
=[(a-b)x+(2a+3b)]/(x-3)(x+2)
=(2x+7)/(x-3)(x+2)
所以(a-b)x+(2a+3b)=2x+7
所以a-b=2
2a+3b=7
所以a=13/5
b=3/5