化简:(3a-2/)+(1-1/)÷(1+1/)

题目

化简:(3a-2/)+(1-1/)÷(1+1/)

答案

原式=[(3a-2)/(a²-a-2)]+[1-1/(a+1)]÷[1+1/(a-1)]
=[(3a-2)/(a²-a-2)]+{ [(a+1)-1]/(a+1) }÷{[(a-1)+1]/(a-1) }
=[(3a-2)/(a²-a-2)]+[a/(a+1)]÷[a/(a-1)]
=[(3a-2)/(a²-a-2)]+[a/(a+1)]×[(a-1)/a]
={ (3a-2)/[(a-2)(a+1)] }+[(a-1)/(a+1)]
={ (3a-2)/[(a-2)(a+1)] }+{(a-1)(a-2)/[(a-2)(a+1)] }
=[(3a-2)+(a-1)(a-2)]/[(a-2)(a+1)]
=(3a-2+a²-3a+2)/[(a-2)(a+1)]
=a²/(a²-a-2)