Question

初二分式题

2.(1)观察下列等式:1/6=1/2×3=1/2-1/3,1/12=1/3-1/4,1/20=1/4×5=1/4-1/5,……由此可以推断1/42=____________;
(2)请用含字母Mde 等式宝石(1)的特点的一般规律;
(3)请用(2)中的规律解下面的方程:
1/(x-2)(x-3) -3/(x-1)(x-4) +1/(x-1)(x-2)=1/x-4

Answer 1

解答：
.(1)观察下列等式:1/6=1/2×3=1/2-1/3,1/12=1/3-1/4,1/20=1/4×5=1/4-1/5,……由此可以推断1/42=1/6-1/7
(2)请用含字母Mde 等式宝石(1)的特点的一般规律;1/[n(n+1)]=1/n-1/(n+1)
(3)请用(2)中的规律解下面的方程:
1/(x-2)(x-3) -3/(x-1)(x-4) +1/(x-1)(x-2)=1/x-4
=1/(x-2)-1/(x-3)+1/(x-4)+1/(x-1)+1/(x-1)-1/(x-2)
=-1/(x-3)+1/(x-4)
=1/[(x-3)(x-4)]

Answer 2

1/6×7=1/6-1/7

1/(x-1)(x-2)=1/(x-1)(x-2)=1/(x-1)-1/(x-2)

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