ГДЗ Алгебра 8 клас Істер (2025)

Спростіть вираз:

1) (x-1)/(x^2- x+1) + (2- x)/(x^3+1) = (x-1)/(x^2- x+1) + (2-x)/(〖(x+1)(x〗^2- x+1)) = (x^2- x+2-x)/(〖(x+1)(x〗^2- x+1)) = (x^2- x+1)/(〖(x+1)(x〗^2- x+1)) = 1/(x+1);
2) 2m/(m-5) – 5/(m+5) + (2m^2)/(25- m^2 ) = 2m/(m-5) – 5/(m+5) – (2m^2)/((m-5)(m+5)) = (2m(m+5)- 5(m-5)- 2m^2)/((m-5)(m+5)) = (2m^2+ 10m-5m+25-2m^2)/((m-5)(m+5)) = (5m+25)/((m-5)(m+5)) = (5(m+5))/((m-5)(m+5)) = 5/(m-5);
3) 6/(m^2- 6m) + (m-12)/(6m-36) = 6/(m(m-6)) + (m-12)/(6(m-6)) = (36+ m^2- 12m)/(6m(m-6)) = ((m-6)^2)/(6m(m-6)) = (m-6)/6m;
4) 3/(2a+6) + (a^2- a-3)/(a^2- 9) – 1 = 3/(2(a+3)) + (a^2- a-3)/((a-3)(a+3)) – 1 = (3(a-3)+ 2(a^2- a-3)- 2(a^2- 9))/(2(a+3)(a-3)) = (3a-9+2a^2- 2a-6-2a^2+ 18)/(2(a+3)(a-3)) = (a+3)/(2(a+3)(a-3)) = 1/(2(a-3)).