Question

(1-2ab/a^2+b^2):a^2-b^2/a^2+b^2

Answer 1

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