ГДЗ Математика 8 клас Істер (2025) - 1 ЧАСТИНА

Спростіть вираз:

1) (a+1)/(a^2+ a+1) + (a+2)/(a^3-1) = (a+1)/(a^2+ a+1) + (a+2)/(〖(a-1)(a〗^2+ a+1))= (a^2- 1+ a+2)/(〖(a-1)(a〗^2+ a+1)) = (a^2+ a+1)/(〖(a-1)(a〗^2+ a+1)) = 1/(a-1);
2) 2a/(a-3) + a/(a+3) + (2a^2)/(9- a^2 ) = 2a/(a-3) + a/(a+3) – (2a^2)/((a-3)(a+3)) = (2a(a+3)+ a(a-3)- 2a^2)/((a-3)(a+3)) = (2a^2+ 6a+ a^2- 3a-2a^2)/((a-3)(a+3)) = (a^2+ 3a)/((a-3)(a+3)) = (a(a+3))/((a-3)(a+3)) = a/(a-3);
3) 4/(m^2+ 4m) + (m+8)/(4m+16) = 4/(m(m+4)) + (m+8)/(4(m+4)) = (16+ m^2+ 8m)/(4m(m+4)) = ((m+4)^2)/(4m(m+4)) = (m+4)/4m;
4) 2/(3b+6) + (b^2- b-2)/(b^2- 4) – 1 = 2/(3(b+2)) + (b^2- b-2)/((b-2)(b+2)) – 1 = (2(b-2)+ 3(b^2- b-2)- 3(b^2- 4))/(3(b-2)(b+2)) =(2b-4+3b^2- 3b-6-3b^2+ 12)/(3(b-2)(b+2)) = (-b+2)/(3(b-2)(b+2)) = –(b-2)/(3(b-2)(b+2)) = –1/(3(b+2)).