Question

Сократите дробь: a^2 + 2ab + b^2/2a^4 - 2b^4

Answer 1

(a^2 + 2ab + b^2)/2a^4 - 2b^4 = (a+b)^2/2(a^2+b^2)*(a^2-b^2) = (a+b)^2/2*(a^2+b^2)*(a+b)*(a-b) = (a+b)/2(a^2+b^2)*(a-b)

Answer 2

a^2+2ab+b^2/2a^4-2b^4=
= (a+b)^2/2(a^4-b^4)=
= (a+b)^2/2(a^2-b^2)(a^2+b^2)=
=(a+b)^2/2(a-b)(a+b)(a^2+b^2)=
=a+b/2(a-b)(a^2+b^2)