已知2x-5/x^2+x-6=A/x+3+B/x-2是恒等式,求A,B的值
问题描述：
已知2x-5/x^2+x-6=A/x+3+B/x-2是恒等式,求A,B的值
答
(2x-5)/(x²+x-6)=A/(x+3)+B/(x-2)(2x-5)/[(x+3)(x-2)]=A(x-2)/[(x+3)(x-2)]+B(x+3)/[(x+3)(x-2)](2x-5)/[(x+3)(x-2)]=(Ax-2A+Bx+3B)/[(x+3)(x-2)](2x-5)/[(x+3)(x-2)]=[(A+B)x+(-2A+3B)]/[(x+3)(x-2)]A+B=2 且 ...