观察下列各式1/2=1/1x2=1/1-1/21/6=1/2x3=1/2-1/31/12=1/3x4=1/3-1/41/20=1/4x5=1/4-1/51/30=1/5x6=1/5-1/6.请你猜想出(1)中的特点的一般规律,用含X(X表示整数)的等式表示出来请利用上述规律计算(有过程)1/2+1/6+1/12.+1/(n-1)n+1/n(n+1)请利用上述规律,解方程1/(x-4)(x-3)+1/(x-3)(x-2)+1/(x-2)(x-1)+1/(x-1)x+1/x(x+1)=1/x+1原方程可以变形如下:

1/(x*(x+1))=1/x-1/(x+1);
An=1/n-1/(1+n);
和=1/1-1/2+1/2-1/3+1/3-1/4……1/(n-1)-1/n+1/n-1/(n+1)=1-1/(n+1);
原方程可化简为：1/(x-4)-1/(x+1)=1/x+1

1/(x-1)x=1/(x-1)-1/x
1/2+1/6+1/12......+1/(n-1)n+1/n(n+1)
=1/1-1/2+1/2-1/3+1/3-1/4+...+1/n-1/(n+1)
=1-1/(n+1)
1/(x-4)(x-3)+1/(x-3)(x-2)+1/(x-2)(x-1)+1/(x-1)x+1/x(x+1)
=1/(x-4)-1/(x-3)+1/(x-3)-1/(x-2)+..+1/x-1/(x+1)
=1/(x-4)-1/(x+1)=1/x+1

1/2+1/6+1/12.+1/(n-1)n+1/n(n+1)
=1/1*2+1/2*3+1/3*4+...+1/(n-1)n+1/n(n+1)
=1-1/2+1/2-1/3+1/3-1/4+...+1/(n-1)-1/n+1/n-1/(n+1)
=1-1/(n+1)
=n/(n+1)
1/(x-4)(x-3)+1/(x-3)(x-2)+1/(x-2)(x-1)+1/(x-1)x+1/x(x+1)=1/x+1
1/(x-4)-1/(x-3)+1/(x-3)-1/(x-2)+1/(x-2)-1/(x-1)+1/(x-1)-1/x+1/x-1/(x+1)=1/(x+1)
1/(x-4)-1/(x+1)=1/(x+1)
1/(x-4)=2/(x+1)
2x-8=x+1
x=9

1/X - 1/(X+1) = 1/ ( X(X+1) )
1/2+1/6+1/12......+1/(n-1)n+1/n(n+1)
= 1/1-1/2+1/2-1/3+1/3-1/4+.....+1/n-1/(n+1)
= n/(n+1).
利用上述规律,解方程
1/(x-4)(x-3)+1/(x-3)(x-2)+1/(x-2)(x-1)+1/(x-1)x+1/x(x+1)=1/x+1
原方程可以变形如下: 1/(x-4)-1/(x+1) = 1/(x+1)
(x+1) = 2x-8
x = 9