Question

解方程1/（x-1）（x-2）+1/（x-2)（x-3）+1/(x-3)(x-4).....1/(x-2011)(x-2012)=2012

另外，化简下面的代数式

1/（x-1）（x-2）+1/（x-2)（x-3）+1/(x-3)(x-4).....1/(x-2011)(x-2012)

Answer 1

1/（x-1）（x-2）+1/（x-2)（x-3）+1/(x-3)(x-4).....1/(x-2011)(x-2012)
=（1/（x-2）-1/（x-1））+（1/（x-3)-1/（x-2））......（1/(x-2012)-1/(x-2011)）
=1/（x-2012）-1/(x-1）
1/（x-2012）-1/(x-1)=2012
X1=（2013+√（2033794876/503））/2
X2=（2013-√（2033794876/503））/2

Answer 2

1/（x-1）（x-2）+1/（x-2)（x-3）+1/(x-3)(x-4).....1/(x-2011)(x-2012)
=1/(x-2012)(x-2011)+1/(x-2011)(x-2000)+......+1/(x-4)(x-3)+1/(x-3)(x-2)+1/(x-2)(x-1)
=1/(x-2012)-1/(x-2011)+1/(x-2011)-1/(x-2000)+...+1/(x-4)-1/(x-3)+1/(x-3)-1/(x-2)+1/(x-2)-1/(x-1)
=1/(x-2012)-1/(x-1)