(a^2+4a/a^2-16):(4a+16/a^2-4a)

[latex]x^2-y^2=(x-y)(x+y) [/latex] [latex] \frac{a^2+4a}{a^2-16} : \frac{4a+16}{a^2-4a} = \frac{a(a+4)}{(a-4)(a+4)} : \frac{4(a+4)}{a(a-4)} = \frac{a}{a-4} : \frac{4(a+4)}{a(a-4)} = \frac{a}{a-4} * \frac{a(a-4)}{4(a+4)} = \\ = \frac{a}{1} * \frac{a}{4(a+4)}= \frac{a^2}{4(a+4)} [/latex]