题目

计算：a²-5a+6/a²-16÷[(a-3/a+4)·(a²-4/a²+5a+4)]

提问时间：2020-10-31

答案

(a²-5a+6)/(a²-16)÷[(a-3)/(a+4)·(a²-4)/(a²+5a+4)]
=(a²-5a+6)/(a²-16)÷[(a-3)(a²-4)/(a+4)(a²+5a+4)]
=(a²-5a+6)/(a²-16)*(a+4)(a²+5a+4)/(a-3)(a²-4)
=(a-2)(a-3)/(a-4)(a+4)*(a+4)(a²+5a+4)/(a-3)(a²-4)
=(a-2)/(a-4)*(a²+5a+4)/(a²-4)
=(a-2)/(a-4)*(a+1)(a+4)/(a-2)(a+2)
=1/(a-4)*(a+1)(a+4)/(a+2)
=(a+1)(a+4)/(a-4)(a+2)
=(a²+5a+4)/(a²-2a-8)