Question

计算:a的平方-16分之a的平方-5a+6除以a的平方+5a+4分之a的平方-4×a-3分之a-4

Answer 1

[(a²-5a+6)/(a²-16)]÷[(a²-4)/(a²+5a+4)]×[(a-4)/(a-3)]
=(a²-5a+6)(a²+5a+4)(a-4)/[(a²-16)(a²-4)(a-3)]
=(a-2)(a-3)(a+1)(a+4)(a-4)/[(a+4)(a-4)(a+2)(a-2)(a-3)]
=(a+1)/(a+2)
=(a+2-1)/(a+2)
=1 -1/(a+2)

Answer 2

[(a²-5a+6)/(a²-16)]÷[(a²-4)/(a²+5a+4)]*[(a-4)/(a-3)]
=[(a-2)(a-3)/(a+4)(a-4)]÷[(a+2)(a-2)/(a+1)(a+4)]*[(a-4)/(a-3)]
=[(a-2)(a-3)/(a+4)(a-4)]*[(a+1)(a+4)/(a+2)(a-2)]*[(a-4)/(a-3)]
=(a+1)/(a+2)