Question

已知x²-7x+10分之3x=x-2分之A+x-5分之B,求A、B的值

Answer 1

因为3x/(x²-7x+10)=A/(x-2)+B/(x-5)

A/(x-2)+B/(x-5)

=A(x-5)/[(x-2)(x-5)]+B(x-2)/[(x-2)(x-5)]

=[A(x-5)+B(x-2)]/[(x-2)(x-5)]

=[(A+B)x-(5A+2B)]/(x²-7x+10)

所以有：3x=(A+B)x-(5A+2B)

有方程组：

A+B=3

5A+2B=0

解方程组,得：

A=-2, B=5