化简1/[x(x+2)]+1/[(x+1)(x+3)]+1/[(X+2)(X+4)].+1/[(X+9)(X+11)]

1/[x(x+2)]+1/[(x+1)(x+3)]+1/[(X+2)(X+4)].+1/[(X+9)(X+11)]
=1/2{1/x-1/(x+2)+1/(x+1)-1/(x+3).+1/(x+9)-1/(x+11)}
=1/2[1/x+1/(x+1)-1/(x+10)-1/(x+11)]
=1/2{[1/x-1/(x+10)]+[1/(x+1)-1/(x+11)]
=1/2{9/[x*(x+10)+10/[(x+1)(x+11)]}
=1/2{(19x^2+208x+99)/[x*(x+1)*(x+10)*(x+11)]}
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原式=1/2[1/X-1/(X+2)+1/(X+1)-1/(X+3)+1/(X+2)-1/(X+4)+……+1/(X+9)-1/(X+11)]
=1/2[1/X+1/(X+1)-1/(X+10)-1/(X+11)]
=……

=1/[x*+2x]+1/[x*+4x+3]+1/[x*+8+6x].......+1/[x*+20x+99]
=1/x+x+2+1/x+x+4+3/x+1/x+x+6+8/x+1/x+99/x+20
=112/x+4x+32/x
=32/x+116
=16/x+58
=8/x+29
x=-8/29