A/x-5+B/x+2=5x-4/x²-3x-10
A(x+2)/(x-5)(x+2)+B(x-5)/(x-5)(x+2)=5x-4/x²-3x-10
(A(x+2)+B(x-5))/(x-5)(x+2))=5x-4/x²-3x-10
(Ax+2A+Bx-5B)/x²-3x-10=5x-4/x²-3x-10
(A+B)x+(2A-5B)/x²-3x-10=5x-4/x²-3x-10
所以A+B=5 2A-5B= -4
解得A=3 B=2