1/(x^(-y)) = 1/(1/x^y) = x^y ⇒
A = {[(a^(1/4) -b^(1/4)]² + 1/[a^(1/4)+b^(1/4)]²} :
:[(√a +√b)]/[(√a -√b)(√a +√b)] =
= {[(a^(1/4) -b^(1/4)]² + 1/[a^(1/4)+b^(1/4)]²} :[1/(√a -√b)] =
= {[(a^(1/4) -b^(1/4)]²·[(a^(1/4) +b^(1/4)]²+1}/{[(a^(1/4) +b^(1/4)]²} :
:[1/(√a -√b)] =
= {[(a^(1/2) - b^(1/2)]² +1} ·[(√a -√b)]/[a^(1/4)+b^(1/4)]² =
= {[(√a -√b)² +1}[a^(1/4)+b^(1/4)·[a^(1/4) - b^(1/4)]/[a^(1/4)+b^(1/4)]²=
={[((√a -√b)]² +1}·[a^(1/4) - b^(1/4)]/[a^(1/4)+b^(1/4)]
={√a -√b]² +1} ·[(√a -√b)]/[√a +2√(√(ab))+√b]