解方程1/(x^2-2x-2)+25/(x^2-2x+2)=24/(x^2-2x+1)

由题意不妨令t=x²-2x+1=(x-1)²,那么：原方程可化为1/(t-3) + 25/(t+1)=24/t上式左边通分得：(t+1+25t-75)/[(t-3)(t+1)]=24/t(26t-74)/[(t-3)(t+1)]=24/t(13t-37)/[(t-3)(t+1)]=12/tt(13t-37)=12(t-3)(t+1)13t²-37t=12t²-24t-36t²-13t+36=(t-4)(t-9)=0解得：t=4或t=9那么：(x-1)²=4或(x-1)²=9所以：x-1=2或x-1=-2或x-1=3或x-1=-3解得：x=3或x=-1或x=4或x=-2经检验可知x=3或x=-1或x=4或x=-2均是原方程的解。