X的倒数为1/X,依题意得,X-1/X=1通分（X²-1）/ X= 1X² - 1 =X X² - X =1则X(X-1)=1,所以X与X-1互为倒数,X+X² =(X-1)+(X-1)²=X-1+X²-2X-1 = X²-X=1 真的!