已知(x-3)/(x+1)(x-1)=A/(x+1)+B/(x-1) 求整数A、B的值

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已知(x-3)/(x+1)(x-1)=A/(x+1)+B/(x-1) 求整数A、B的值

已知(x-3)/(x+1)(x-1)=A/(x+1)+B/(x-1) 求整数A、B的值
已知(x-3)/(x+1)(x-1)=A/(x+1)+B/(x-1) 求整数A、B的值

已知(x-3)/(x+1)(x-1)=A/(x+1)+B/(x-1) 求整数A、B的值
1/(x+1) - 1/(x-1) = -2/(x+1)(x-1)
(x-3)/(x+1)(x-1)
= [(x-1)-2] / (x+1)(x-1)
= (x-1)/(x+1)(x-1) - 2/(x+1)(x-1)
= 1/(x+1) + [1/(x+1) - 1/(x-1)]
= 2/(x+1) - 1/(x-1)
A = 2
B = -1