已知1/x+1/y=1/(x-y) 求(x+y)/x-(x-y)/y+6的值

来源:学生作业帮助网 编辑:作业帮 时间:2024/04/30 14:27:33
已知1/x+1/y=1/(x-y) 求(x+y)/x-(x-y)/y+6的值

已知1/x+1/y=1/(x-y) 求(x+y)/x-(x-y)/y+6的值
已知1/x+1/y=1/(x-y) 求(x+y)/x-(x-y)/y+6的值

已知1/x+1/y=1/(x-y) 求(x+y)/x-(x-y)/y+6的值
1/x+1/y=(x+y)/xy=1/(x-y)
(x+y)(x-y)=x²-y²=xy
原式=(xy+y²-x²+xy)/xy+6
=[-(x²-y²)+2xy]/xy+6
=(-xy+2xy)/xy=6
xy/xy+6
=1+6
=7

1/x+1/y=1/(x-y)
→x/y-y/x=1.
∴(x+y)/x-(x-y)/y+6
=8-(x/y-y/x)
=8-1
=7。