Question

一道化简题

｛【（a²-a）／（a－1）】－【a／（a＋1）】｝÷｛1+【1/（a²-1）】｝

Answer 1

原式={a（a-1）/（a-1）-a/(a+1)}÷{1+1/（a²-1）}
={a-a/(a+1)}/{（a²-1）}÷{（a²-1）+1/（a²-1）}
={a(a+1)/(a+1)-a/(a+1)}÷{【（a²-1）+1】/（a²-1）}
={【a(a+1)-a】/(a+1)}÷{a²/（a²-1）}
={a²/(a+1)}÷{a²/（a²-1）}
={a²/(a+1)}÷{a²/（a+1）（a-1）}
={a²（a-1）/(a+1)（a-1）}÷{a²/（a+1）（a-1）}
=a²（a-1）（a+1）（a-1）/a²(a+1)（a-1）
=a-1

Answer 2

原式=[a(a-1)/(a-1)]-[a/(a+1)]÷[(a²-1+1)/(a²-1)]
=a-[a/(a+1)]×[(a+1)(a-1)/a²]
=a-(a-1)/a
=(a²-a+1)/a