Question

Упростите выражение
2mn/m^3+n^3+2m/m^2-n^2-1/m-n

Answer 1

Общий знаменатель (m-n)(m+n)(m²-mn+n²)
(2mn*(m-n)+2m(m²-mn+n²)-1(m³+n³))/(m-n)(m+n)(m²-mn+n²)=
(2m²n-2mn²+2m³-2m²n+2mn²-m³-n³)/(m-n)(m+n)(m²-mn+n²)=
(m³-n³)/(m-n)(m+n)(m²-mn+n²)=(m-n)(m²+mn+n²)/(m-n)(m+n)(m²-mn+n²)=
(m²+mn+n²)/(m+n)(m²-mn+n²)=(m²+mn+n²)/(m³-n³)