ГДЗ Алгебра 8 клас Істер (2025)

Спростіть вираз:

1) (16-7a)/((3-a)^2 ) – (13-6a)/((a-3)^2 ) = (16-7a)/((3-a)^2 ) – (13-6a)/((3-a)^2 ) = (16-7a-(13-6a))/((3-a)^2 ) = (16-7a-13+6a)/((3-a)^2 ) = (3-a)/((3-a)^2 ) = 1/(3-a);
2) (15(2m -3))/((3-m)^3 ) + (5m^2)/((m-3)^3 ) = (5m^2)/((m-3)^3 ) – (15(2m-3))/((m-3)^3 ) = (5m^2- 30m+45)/((m-3)^3 ) = (5(m^2- 6m+9))/((m-3)^3 ) = (5(m-3)^2)/((m-3)^3 ) = 5/(m-3);
3) (p^2- 9q)/((p-3)(q-4)) – (3(p-3q))/((3-p)(4-q)).
Оскільки (3 – p)(4 – q) = (–(p – 3)) • (–(q – 4)) = (p – 3)(q – 4), то маємо (p^2- 9q)/((p-3)(q-4)) – (3(p-3q))/((3-p)(4-q)) = (p^2- 9q-3p+9q)/((p-3)(q-4)) = (p^2- 3p)/((p-3)(q-4)) = (p(p-3))/((p-3)(q-4)) = p/(q-4).