Сначала упростим выражение:
5n^2 / (n+1)^2 (2n^2 - 2) / 15n^= 5n^2 (2n^2 - 2) / 15n^2 (n+1)^= 5n^2 (2n^2 - 2) / 15n^2 (n^2 + 2n + 1= 5n^2 (2n^2 - 2) / 15n^2 (n + 1)^= 5n^2 (2n^2 - 2) / 15n^2 (n^2 + 2n + 1= 5n^2 2n^2 - 5n^2 2 / 15n^2 n^2 + 15n^2 2n + 15n^2 = 10n^4 - 10n^2 / 15n^2 - 30n + 15n^= (10n^4 - 10n^2) / (15n^2) - 30n + 1= 10n^2( n^2 - 1) / 15n^2 - 30n + 1= (10n^2(n+1)(n-1)) / 15n^2 - 30n + 1= (10/15)(n+1)(n-1) - 30n + 1= 2/3(n+1)(n-1) - 30n + 1= (2n^2 - 2) / 3 - 30n + 1= 2n^2 / 3 - 2 / 3 - 30n + 1= 2n^2 / 3 - 2 / 3 - 90n / 3 + 1= 2n^2 / 3 - 2 / 3 - 30n + 15
Ответ: 2n^2 / 3 - 2 / 3 - 30n + 15.
Сначала упростим выражение:
5n^2 / (n+1)^2 (2n^2 - 2) / 15n^
= 5n^2 (2n^2 - 2) / 15n^2 (n+1)^
= 5n^2 (2n^2 - 2) / 15n^2 (n^2 + 2n + 1
= 5n^2 (2n^2 - 2) / 15n^2 (n + 1)^
= 5n^2 (2n^2 - 2) / 15n^2 (n^2 + 2n + 1
= 5n^2 2n^2 - 5n^2 2 / 15n^2 n^2 + 15n^2 2n + 15n^2
= 10n^4 - 10n^2 / 15n^2 - 30n + 15n^
= (10n^4 - 10n^2) / (15n^2) - 30n + 1
= 10n^2( n^2 - 1) / 15n^2 - 30n + 1
= (10n^2(n+1)(n-1)) / 15n^2 - 30n + 1
= (10/15)(n+1)(n-1) - 30n + 1
= 2/3(n+1)(n-1) - 30n + 1
= (2n^2 - 2) / 3 - 30n + 1
= 2n^2 / 3 - 2 / 3 - 30n + 1
= 2n^2 / 3 - 2 / 3 - 90n / 3 + 1
= 2n^2 / 3 - 2 / 3 - 30n + 15
Ответ: 2n^2 / 3 - 2 / 3 - 30n + 15.