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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
题目详情
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
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
▼优质解答
答案和解析
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
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
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