ГДЗ Алгебра 8 клас Мерзляк (2025)

Виконайте дії:

1) 3/(x+3) + (x+4)/(x^2-9) = 3^(\x-3)/(x+3) + (x+4)/((x-3)(x+3)) = (3(x-3)+(x+4))/((x- 3)(x+3)) = (3x-9+ x+4)/((x-3)(x+3)) = (4x-5)/(x^2-9);
2) a^2/(a^2-64) – a/(a-8) = a^2/((a-8)(a+8)) – a^(\a+8)/(a-8) = (a^2-a(a+8))/((a-8)(a+8)) = (a^2-a^2-8a)/((a-8)(a+8)) = –8a/(a^2-64) = 8a/(64-a^2 );
3) 6b/(9b^2-4) – 1/(3b-2) = 6b/((3b-2)(3b+2)) – 1^(\3b+2)/(3b-2) = (6b-(3b+2))/((3b-2)(3b+2)) = (6b-3b-2)/((3b-2)(3b+2)) = (3b-2)/((3b-2)(3b+2)) = 1/(3b+2);
4) m/(m+5) – m^2/(m^2+10m+25) = m^(\m+5)/(m+5) – m^2/((m+5)^2 ) = (m(m+5)-m^2 )/((m+5)^2 ) = (m^2+5m-m^2 )/((m+5)^2 ) = 5m/((m+5)^2 ).