ГДЗ Алгебра 8 клас Мерзляк (2025)

Виконайте дії:

1) (a+b)/(c-7) + a/(7-c) = (a+b)/(c-7) + a/(-(c-7)) = (a+b)/(c-7) – a/(c-7) = (a+b-a)/(c-7) = b/(c-7);
2) 5m/(m-n) + 5n/(n-m) = 5m/(m-n) + 5n/(-(m-n)) = 5m/(m-n) – 5n/(m-n) = (5m-5n)/(m-n) = (5(m-n))/(m-n) = 5;
3) (2x-4y)/(x-3y) – (4x-14y)/(3y-x) = (2x-4y)/(x-3y) – (4x-14y)/(-(x-3y)) = (2x-4y)/(x-3y) + (4x-14y)/(x-3y) = ((2x-4y)+ (4x-14y))/(x-3y) = (2x-4y+4x-14y)/(x-3y) = (6x-18y)/(x-3y) = (6(x-3y))/(x-3y) = 6/1 = 6;
4) (81b^2)/(9b-a) + a^2/(a-9b) = (81b^2)/(9b-a) + a^2/(-(9b-a)) = (81b^2)/(9b-a) – a^2/(9b-a) = (81b^2- a^2)/(9b-a) = ((9b-a)(9b+a))/(9b-a) = (9b+a)/2 = 9b + a;
5) t^2/(3t-6) + 4/(6-3t) = t^2/(3t-6) + 4/(-(3t-6)) = t^2/(3t-6) – 4/(3t-6) – 4/(3t-6) = (t^2- 4)/(3t-6) = ((t-2)(t+2))/(3(t-2)) = (t+2)/2;
6) y^2/(y-1) – (1-2y)/(1-y) = y^2/(y-1) – (1-2y)/(-(y-1)) = y^2/(y-1) + (1-2y)/(y-1) = (y^2+ 1-2y)/(y-1) = ((y-1)^2)/(y-1) = (y-1)/1 = y – 1.