Question

（1）观察下列各式：1/6=1/2*1/3=1/2-1/3,1/12=1/3*1/4=1/3-1/4 1/20=1/4*

Answer 1

1.1/(n*(n+1))=1/n*1/(n+1)=1/n-1/(n+1);

理由的话你可以反推啊,先通分再消掉式子就可以了.

2.1/（x-2)*1/(x-3)-2/(x-1）*（x-3)+1/(x-1)(x-2)

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

=1/(x-3)-1/(x-1)-2/(x-1)*(x-3)

=2/(x-3)*(x-1)-2/(x-1)*(x-3)

=0