Question

$frac{a}{ab+2b^{2}}:frac{4a^{2}}{a^{2}+4ab+4b^{2}}$

Answer 1

$frac{a}{ab+2b^2}:frac{4a^2}{a^2+4ab+4b^2}=\ frac{a}{ab+2b^2}*frac{a^2+4ab+4b^2}{4a^2}=\ frac{a(a^2+4ab+4b^2)}{4a^2(ab+2b^2)}=\ frac{a(a+2b)^2}{4a^2b(a+2b)}=\ frac{a+2b}{4ab}$