Question

观察下列各式，1/1*2=1-1/2 1/2*3=1/2-1/3，1/3*4=1/3-1/4

用上列变化规律解方程
1/(x(x-1))+1/((x-1)(x-2))+.......+1/((x-9)(x-10))=5/12

Answer 1

化简成1/(x-1)-1/x+1/(x-2)-1/(x-1)+…+1/(x-10)-1/(x-9)=5/12
1/(x-10)-1/x=5/12
10/(x(x-10))=5/12
x=12

Answer 2

那下面全化成上面形式 最后x=？咦题目不对啊

Answer 3

1/(x(x-1))=1/(x-1) -1/x，拆项相销可得方程为1/(x-10)-1/x=10/(x(x-10))=5/12.解得x=12或-2

Answer 4

同样的都裂开，得1/(x-10)-1/x=5/12，解得x=12。

Answer 5

Answer 6

左式=1/x-1/(x-1)+1/(x-1)-1/(x-2)+……+1/(x-9)-1/(x-10)=1/x-1/(x-10),这样就变成了一元二次方程。