麻烦问题表述的时候最好加上括号.
你想求的是这样：[(a-4)/(a²-9)] ÷ [1/(a-3)] × [(a²-6a+9)/(a²-16)] ,
还是这样：[(a-4)/(a²-9)] ÷ {[1/(a-3)] × [(a²-6a+9)/(a²-16)]} ,
或者是这样：a²-a/9-4÷a-(1/3)*a²-a²/16-6a+9
当然还有其他形式!
[(a-4)/(a²-9)] ÷ [1/(a-3)] × [(a²-6a+9)/(a²-16)]
={(a-4)/[(a+3)(a-3)]} × (a-3) × {(a²-6a+9)/[(a+4)(a-4)]}
=[(a-4)/(a+3)] × {(a²-6a+9)/[(a+4)(a-4)]}
=(a²-6a+9)/[(a+3)(a+4)]
=(a²-6a+9)/(a²+7a+12)
[(a-4)/(a²-9)] ÷ {[1/(a-3)] × [(a²-6a+9)/(a²-16)]}
=[(a-4)/(a²-9)] ÷ {[1/(a-3)] × [(a-3)²/(a²-16)]}
=[(a-4)/(a²-9)] ÷ [(a-3)/(a²-16)]
=[(a-4)/(a²-9)] × [(a²-16)/(a-3)]
=[(a-4)(a²-16)]/[(a²-9)(a-3)]
=(a³-4a²-16a+64)/(a³-3a²-9a+27)
a²-a/9-4÷a-(1/3)*a²-a²/16-6a+9
=a²-a/9-4/a-a²/3-a²/16-6a+9
=(1-1/3-1/16)a²-(1/9+6)a+9-4/a
=(29/48)a²-(55/9)a+9-4/a
=[(29/48)a³-(55/9)a²+9a-4]/a