ГДЗ Алгебра 8 клас Істер (2025)

Спростіть вираз:

1) (a+4)/(ab- a^2 ) + (b+4)/(ab- b^2 ) = (a+4)/(a(b-a)) – (b+4)/(b(b-a)) = (ab+4b-ab-4a)/(ab(b-a)) = (4(b-a))/(ab(b-a)) = 4/ab;
2) m^2/(mx- x^2 ) + x/(x-m) = m^2/(x(m-x)) – x/(m-x) = (m^2- x^2)/(x(m-x)) = ((m-x)(m+x))/(x(m-x)) = (m+x)/x;
3) 2/(x^2- 4) – 1/(x^2+ 2x) = 2/((x-2)(x+2)) – 1/(x(x+2)) = (2x-(x-2))/(x(x-2)(x+2)) = (2x-x+2)/(x(x-2)(x+2)) = (x+2)/(x(x-2)(x+2)) = 1/(x^2- 2x);
4) (3ab-27a^2)/(b^2- 3ab) – (3a^2- b^2)/(ab-3a^2 ) = (3ab-27a^2)/(b(b-3a)) – (3a^2- b^2)/(a(b-3a)) = (3a^2 b-27a^3- 3a^2 b+ b^3)/(ab(b-3a)) = (b^2+ 27a^3)/(ab(b-3a)) = ((b-3a)(b^2+ 3ab+ 9a^2))/(ab(b-3a)) = (b^2+ 3ab+9a^2)/ab.