ГДЗ Алгебра 8 клас Мерзляк (2025)

Спростіть вираз:

1) (5n-1)/20n – (7n-8)/20n – (8n+7)/20n = ((5n-1)- (7n-8)- (8n+7))/20n = (5n-1-7n+8-8n-7)/20n = (-10n)/20n = –1/2;
2) (9m+2)/(m^2- 4) – (m-9)/(4- m^2 ) + (1-7m)/(m^2- 4) = (9m+2)/(m^2- 4) + (m-9)/(m^2- 4) + (1-7m)/(m^2- 4) = ((9m+2)+ (m-9)+ (1-7m))/(m^2- 4) = (9m+2+m-9+1-7m)/(m^2- 4) = (3m-6)/(m^2- 4) = (3(m-2))/((m-2)(m+2)) = 3/(m+2);
3) 3k/(k^3- 1) + (4k+1)/(1- k^3 ) + k^2/(1- k^3 ) = 3k/(k^3- 1) – (4k+1)/(k^3- 1) – k^2/(k^3- 1) = (3k-(4k+1)- k^2)/(k^3- 1) = (3k-4k-1- k^2)/(k^3- 1) = (-k-1- k^2)/(k^3- 1) = (-(k^2+ k+1))/((k-1)(k^2+ k+1)) = –1/(k-1) = 1/(1-k).