ГДЗ Математика 8 клас Істер (2025) - 1 ЧАСТИНА

Спростіть вираз:

1) (a-2)/(ab- a^2 ) – (2-b)/(ab- b^2 ) = (a-2)/(a(b-a)) + (2-b)/(b(b-a)) = (ab-2b+2a-ab)/(ab(b-a)) = (2(a-b))/(-ab(a-b)) = –2/ab;
2) t^2/(ta+ a^2 ) – a/(t+a) = t^2/(a(t+a)) – a/(t+a) = (t^2- a^2)/(a(t+a)) = ((t-a)(t+a))/(a(t+a)) = (t-a)/a;
3) 4/( a^2- 9) – 2/(a^2+ 3a) = 4/((a-3)(a+3)) – 2/(a(a+3)) = (2(a+3))/(a(a-3)(a+3)) = 2/(a^2- 3a);
4) (3n^2- 8m^2)/(n^2- 2mn) – (3mn- n^2)/(mn-2m^2 ) = (3n^2- 8m^2)/(n(n-2m)) – (3mn- n^2)/(m(n-2m)) = (3n^2 m-8m^3- 3mn^2+ n^3)/(mn(n-2m)) = (n^3- 8m^3)/(mn(n-2m)) = ((n-2m)(n^2+ 2mn+4m^2))/(mn(n-2m)) = (n^2+ 2mn+4m^2)/mn.