天才，帮帮我！！初二数学

来源：百度知道 编辑：UC知道 时间：2024/05/24 20:30:07
1.已知x=10,求1/x-1+1/(x-1)(x-2)+1/(x-2)(x-3)+1/(x-3)(x-4)+1/(x-4)(x-5)的值
2.已知1/x=1/a+1/b,1/y=1/b-1/a,求x/y的值

1.已知x=10,求1/x-1+1/(x-1)(x-2)+1/(x-2)(x-3)+1/(x-3)(x-4)+1/(x-4)(x-5)的值

1/(x-1)(x-2)=1/(x-1)-1/(x-2)
1/(x-2)(x-3)=1/(x-2)-1/(x-3)
1/(x-3)(x-4)=1/(x-3)-1/(x-4)
1/(x-4)(x-5)=1/(x-4)-1/(x-5)

原式=1/x-1+1/(x-1)-1/(x-5)
=1/10-1+1/9-1/5
=-89/90

2.已知1/x=1/a+1/b,1/y=1/b-1/a,求x/y的值

1/x=(a+b)/(ab)........x=ab/(a+b)
1/y=(a-b)/(ab)

x/y=(a-b)/(a+b)