[1+1/(x-1)]/[1+1/(x^2-1)=.[(x-1)/(x-1)+1/(x-1)]/[(x^2-1)/(x^2-1)+1/(x^2-1)=[(x-1+1)/(x-1)]/[(x^2-1+1)/(x^2-1)]=[x/(x-1)]/[x^2/(x^2-1)]=[x/(x-1)]*[(x+1)(x-1)/x^2]=(x+1)/x