Question

若(x+2)(x+3)分之3x+5=x+2分之A+x+3分之B,求A B的值

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Answer 1

(3x+5)/[(x+2)(x+3)]=A/(x+2) +B/(x+3)
(3x+5)/[(x+2)(x+3)]=[A(x+3)+B(x+2)]/[(x+2)(x+3)]

(3x+5)/[(x+2)(x+3)]=[(A+B)x+(3A+2B)]/[(x+2)(x+3)]

要等式对于任意使分式有意义的x恒成立，只有
A+B=3
3A+2B=5
解得A=-1 B=4

Answer 2

解由x+2分之A+x+3分之B
=A/(x+2)+B/(x+3)
=A(x+3)/(x+2)(x+3)+B(x+2)/(x+3)(x+2)
=[A(x+3)+B(x+2)]/(x+3)(x+2)
=[(A+B)x+3A+2B)]/(x+3)(x+2)
=(x+2)(x+3)分之3x+5
即(A+B)x+3A+2B=3x+5
即A+B=3,
3A+2B=5
解得A=-1,B=4

Answer 3

若(x+2)(x+3)分之3x+5=x+2分之A+x+3分之B,求A B的值 解：(3x+5)/(x+2)(x+3)=A/(x+2)+B/(x+3)右边A/(x+2)+B/(x+3)通分得[A(x+3)+B(x+2)]/(x+2)(x+3)=[(A+B)x+3A+2B]/(x+2)(x+3)所以A+B=3，3A+2B=5 联立方程可得A=-1， B=4这种方法类似待定系数法，也可以成为待定系数法的一种应用，经常用没有什么的，能帮助到你我很开心！

Answer 4

若(x+2)(x+3)分之3x+5=x+2分之A+x+3分之B,求A B的值解：(3x+5)/(x+2)(x+3)=A/(x+2)+B/(x+3)右边A/(x+2)+B/(x+3)通分得[A(x+3)+B(x+2)]/(x+2)(x+3)=[(A+B)x+3A+2B]/(x+2)(x+3)所以A+B=3，3A+2B=5 联立方程可得A=-1， B=4