(1)已知(1／x) -(1／y)=3,则代数式(2x-14xy-2y)／(x-2xy-y)的值为_____.(2)若1／x(x+1)=(A／x)+(B／x+1),则A=_______,B=_______.(3)分解因式：(2x)／(x^-4)+3／(x+2)+1／(2-x)；
来源：学生作业帮助网 编辑：六六作业网 时间：2024/12/25 22:30:22
(1)已知(1／x) -(1／y)=3,则代数式(2x-14xy-2y)／(x-2xy-y)的值为_____.(2)若1／x(x+1)=(A／x)+(B／x+1),则A=_______,B=_______.(3)分解因式：(2x)／(x^-4)+3／(x+2)+1／(2-x)；
(1)已知(1／x) -(1／y)=3,则代数式(2x-14xy-2y)／(x-2xy-y)的值为_____.
(2)若1／x(x+1)=(A／x)+(B／x+1),则A=_______,B=_______.
(3)分解因式：(2x)／(x^-4)+3／(x+2)+1／(2-x)；
(1)已知(1／x) -(1／y)=3,则代数式(2x-14xy-2y)／(x-2xy-y)的值为_____.(2)若1／x(x+1)=(A／x)+(B／x+1),则A=_______,B=_______.(3)分解因式：(2x)／(x^-4)+3／(x+2)+1／(2-x)；
1/x-1/y=3
(y-x)/(xy)=3
y-x=3xy
x-y=-3xy
(2x-14xy-2y)/(x-2xy-y)
=[2(x-y)-14xy]/[(x-y)-2xy]
=(-6xy-14xy)/(-3xy-2xy)
=-20xy/(-5xy)
=4
A/x+B/(x+1)
=[A(x+1)+Bx]/x(x+1)
=[(A+B)x+A]/x(x+1)
=1/x(x+1)
所以A+B=0,A=1
A=1,B=-1
(2x)/(x^2-4)+3/(x+2)+1/(2-x)
=(2x)/(x+2)(x-2)+3/(x+2)-1/(x-2)
=[2x+3(x-2)-(x+2)]/(x+2)(x-2)
=(2x+3x-6-x-2)/(x+2)(x-2)
=(4x-8)/(x+2)(x-2)
=4(x-2)/(x+2)(x-2)
=4/(x+2)