分式的运算1.3x+4/(x+3)(x+2)=A/（x+3）-B(x-2)[A.B为整数]求A.B的值2.已知x-3y=0,求（2x+y）/(x^2-2xy+y^2)*(x-y)的值

Question

分式的运算
1.
3x+4/(x+3)(x+2)=A/（x+3）-B(x-2)[A.B为整数]求A.B的值
2.
已知x-3y=0,求（2x+y）/(x^2-2xy+y^2)*(x-y)的值

Answer 1

1.
3x+4/(x+3)(x+2)=A/（x+3）-B(x-2)
3x+4=A(x-2)-B(x+3)
3x+4=(A-b)x+(-2A-3B)
A-B=3
-2A-3B=4
解方程组得：
A=1,B=-2
2)
x-3y=0
x=3y
（2x+y）/(x^2-2xy+y^2)*(x-y)
=(2x+y)/(x-y)
=(6y+y)(3y-y)
=7y/2y
=7/2