№4 ((1/(m-1))-((m+1)/(m^2+m+1))):(1+(1/(n^3-1)))

( (1 / (m - 1) - ( (m + 1) / (m² + m + 1) ) ) : (1 + (1 / (m³ - 1) ) ),

Сведем к общему знаменателю (m - 1) * (m² + m + 1) и (m³ - 1) :

( ( (1 * (m² + m + 1) - (m + 1) * (m - 1) ) / ( (m - 1) * (m² + m + 1) ) ) : ( (1 * (m³ - 1) + 1 ) / (m³ - 1) ) =

( m² + m + 1 - m² + 1) / (m³ - 1 ) : ( (m³ - 1 + 1) / (m³ - 1) ) =

(m + 2) / (m³ - 1 ) : (m³ / (m³ - 1) ) =

(m + 2) / (m³ - 1 ) * ( (m³ - 1) / m³ ) =

(m + 2) / m^3 .

^{Ответ: (m + 2) / m3 .}