计算：(a^2-8a+16)/(9-a^2 ) ÷(16-a^2)/(9+6a+a^2 )

计算：(a^2-8a+16)/(9-a^2 ) ÷(16-a^2)/(9+6a+a^2 )
计算：(a^2-8a+16)/(9-a^2 ) ÷(16-a^2)/(9+6a+a^2 )

计算：(a^2-8a+16)/(9-a^2 ) ÷(16-a^2)/(9+6a+a^2 )
原式=(a-4)²/(a+3)(a-3)÷[-(a+4)(a-4)/(a+3)²]
=-(a-4)²/(a+3)(a-3)×(a+3)²/(a+4)(a-4)
=-(a-4)/(a-3)×(a+3)/(a+4)
=(-a²+a+12)/(a²+4a-12)

：(a^2-8a+16)/(9-a^2 ) ÷(16-a^2)/(9+6a+a^2 )
=(a-4)²×(a+3)²÷[﹙a+3)(a-3)(a+4)(a-4)
=(a-4)(a+3)÷[(a-3)(a+4)
=(a²-a-12)/(a²+a-12)

(a^2-8a+16)/(9-a^2 ) ÷(16-a^2)/(9+6a+a^2 )
(a-4)^2/(3-a ) (3+a ) ÷(4-a ) (4+a )/ (3+a )^2
=(a-4)^2/(3-a ) (3+a )*(3+a )^2/(4-a ) (4+a )
=[(4-a)/(3-a )]*[(3+a )/ (4+a )]
=(3+a )(4-a)/(3-a )(4+a )