(x-1)(x+2)分之2x-3=x-1分之A加x+2分之B 求A B的值

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(x-1)(x+2)分之2x-3=x-1分之A加x+2分之B 求A B的值

(x-1)(x+2)分之2x-3=x-1分之A加x+2分之B 求A B的值
(x-1)(x+2)分之2x-3=x-1分之A加x+2分之B 求A B的值

(x-1)(x+2)分之2x-3=x-1分之A加x+2分之B 求A B的值
(2x-3)/(x-1)(x+2)=A/(x-1)+B/(x+2)
通分得:(2x-3)/(x-1)(x+2)=A(x+2)/(x-1)(x+2)+B(x-1)/(x-1)(x+2)
去分母得;2x-3=A(x+2)+B(x-1)
去括号得:2x-3=Ax+2A+Bx-B
整理得:2x-3=(A+B)x+2A-B
要使上面等式成立,则要满足:
A+B=2 2A-B=-3
解得:
A=-1/3 B=7/3