解方程：1/(x-1)(x+1)+1/(x+1)(x+3)+1/(x+3)(x+5)=1

拆项法,1/(x-1)(x+1)=0.5[1/(x-1)-1/(x+1)]
1/(x+1)(x+3)=0.5[1/(x+1)-1/(x+3)]
1/(x+3)(x+5)=0.5[1/(x+3)-1/(x+5)]
所以方程化为：0.5[1/(x-1)-1/(x+5)]=1
3/(x-1)(x+5)=1
x^2+4x-5=3
x^2+4x-8=0
x=-2±2√3