Question

若(x-3)/(x+2)(x-1)=A/(x+1)+B/(x-1),求A,B的值

Answer 1

x-3/(x+1)(x-1)=A/x+1+B/x-1
x-3/(x+1)(x-1)=A(x-1)+B(x+1)/(x+1)(x-1)
x-3/(x+1)(x-1)=((A+B)x-A+B)/(x+1)(x-1)
A+B=1 -A+B=-3
A=2 B=-1
AB=-2

追问

sorry啊，老师说这题目错啦

Answer 2

（x-3）（x+1)=(x+2)(Ax-A+Bx+B)
化简得到：x^2-2x-3=（A+B）x^2+（3B+2A）x+（2B-2A）
得方程组：A+B=1
3B+A=-3
解得:A=-1/2
B=5/4
应该是这样的，大概。(*^__^*) 嘻嘻……