ГДЗ Алгебра 8 клас Мерзляк (2025)

Доведіть тотожність:

1) (a+3)/(a^2- 3a) + (a-3)/(3a+9) + 12/(9- a^2 ) = (a-3)/3a; (a+ 3^(\3(a+3)))/(a(a-3)) + (a- 3^(\a(a-3)))/(3(a+3)) – 12^(\3a)/((a-3)(a+3)) = (3(a+3)^2+ a(a-3)^2- 36a)/(3a(a-3)(a+3)) = (3a^2+ 18a+27+ a^3- 6a^2+ 9a-36a)/(3a(a-3)(a+3)) = (a^3- 3a^2- 9a+27)/(3a(a-3)(a+3)) = (a^2 (a-3)- 9(a-3))/(3a(a-3)(a+3)) = ((a-3)(a^2- 9))/(3a(a-3)(a+3)) = ((a-3)(a^2- 9))/(3a(a^2- 9)) = (a-3)/3a;
2) (b-4)/(2a-1) – (b^2- 2b-24)/(2ab-4-b+8a) = 2/(2a-1); (b-4)/(2a-1) – (b^2- 2b-24)/(b(2a-1)+ 4(2a-1)) = 2/(2a-1); (b- 4^(\b+4))/(2a-1) – (b^2- 2b- 24^(\1))/((2a-1)(b+4)) = 2/(2a-1); (b^2- 16- b^2+ 2b+24)/((2a-1)(b+4)) = 2/(2a-1); (2(b+4))/((2a-1)(b+4)) = 2/(2a-1); 2/(2a-1) = 2/(2a-1). Тотожність доведено.