数学求值~

来源：百度知道 编辑：UC知道 时间：2024/06/03 20:08:45
1.已知(1-x)和(y+1)互为倒数,求1/x-1/y的值

2.已知1/a-1/b=4,求a-2ab-b/2a-2b+7ab的值

3.已知1/a+1/b=1/a+b,求a/b+b/a的值
拜托拜托~我急用哈!!!会一题的也告诉下来~~~多谢多谢~~!!!

(1-x)与(y+1)互为倒数
(1-x)*(y+1)=1
1-x+y-xy=1,即：xy=y-x
1/y-1/x=(x-y)/xy,且xy=y-x
1/y-1/x=-1
1/x-1/y=1

1/a-1/b=4，
(b-a)/(ab)=4,
b-a=4ab,
a-b=-4ab,
(a-2ab-b)/(2a-2b+7ab)
=[(a-b)-2ab]/[2(a-b)+7ab]
=(-4ab-2ab)/(-8ab+7ab)
=(-6ab)/(-ab)
=6.

1/a+1/b=1/(a+b)
乘以a+b,(1/a+1/b)(a+b)=1
去括号, b/a+a/b+1+1=1
移项, b/a+a/b=-1

1-x=1/(y+1)
(1-x)(y+1)=1
y+1-xy-x=1
y-x=xy
1/x-1/y=1

(b-a)/ab=4
b-a=4ab
(a-2ab-b)/(2a-2b+7ab)
=-6ab/(-ab)
=6

(a+b)/ab=1/(a+b)
a^2+b^2+2ab=ab
a^2+b^2=-ab
a/b+b/a
=(a^2+b^2)/ab
=-1

1. 1
2. 6
3. -1

(1-x)*(y+1)=1
1-x+y-xy=1
xy=y-x
1/x-1/y=1

1/a-1/b=4

(a-2ab-b)/(2a-2b+7ab)=ab(1/b-2-1/a)/ab(2/b-2/a+7)
=(1/b-1/a-2)/(2/b-2/a+7)
=(-4-2)/(-8+7)
=6

1/a+1/b=1/(a+b)

(a+b)b+(a+b)a=ab