【急】3道七年级数学题目(特殊分式）

① 1/1*2+1/2*3+1/3*4+……91/98*99+1/99*100
=(1-1/2)+(1/2-1/3)+(1/3-1/4)+……+(1/99-1/100)
中间抵消
=1-1/100
=99/100
② 化简下列算是：1/x+1/x(x+1)+1/(x+1)(x+2)+……+1/(x+2004)(x+2005)
1/x(x+1)=[(x+1)-x]/x(x+1)=(x+1)/x(x+1)-x/x(x+1)=1/x-1/(x+1)
其他以此类推
原式=1/x+[1/x-1/(x+1)]+[1/(x+1)-1/(x+2)]+……+[1/(x+20047)-1/(x+2005)]
=1/x+1/x-1/(x+2005)
=(x+4010)/x(x+2005)
③ 求下列分式方程 1/x(x+2)+1/(x+2)(x+4)-1/2x=1
1/2[1/x-1/(x+2)]+1/2[(1/(x+2)-1/(x+4)]-1/2x=1
1/2[1/x-1/(x+2)+(1/(x+2)-1/(x+4)]-1/2x=1
1/2[1/x-1/(x+4)]-1/2x=1
1/2x-1/[2(x+4)]-1/2x=1
-1/[2(x+4)]=1
x+4=-1/2
x=-9/2