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

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

3/（x+1)(x-2)=(Ax+B)/(x+1)+C/(x-2),求A,B,C的值
3÷(x+1)(x+2)=(Ax+B)÷(x+1)+C÷(x-2)
两边同时乘以(x+1)(x+2),得
3=(Ax+B)(x+2)+C(x-1)
Ax²+(B+2A+C)x+(2B-C)=3
对应系数相等
A=0
B+2A+C=0
2B-C=3
解得A=0,B=1,C=-1
回答满意请采纳~

a=0 b=-1 c=1