Question

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

Answer 1

$x^2-y^2=(x-y)(x+y)$

$frac{a^2+4a}{a^2-16} : frac{4a+16}{a^2-4a} = frac{a(a+4)}{(a-4)(a+4)} : frac{4(a+4)}{a(a-4)} = frac{a}{a-4} : frac{4(a+4)}{a(a-4)} = frac{a}{a-4} * frac{a(a-4)}{4(a+4)} = \ = frac{a}{1} * frac{a}{4(a+4)}= frac{a^2}{4(a+4)}$