ГДЗ Алгебра 9 клас Істер НУШ

18. Виконайте дію:

1) (3x(x - 1))/(〖9x〗^2 - y^2 ) + (xy - y)/(y^2 - 〖9x〗^2 ) = (3x(x - 1))/(〖9x〗^2 - y^2 ) – (xy - y)/(〖9x〗^2 - y^2 ) = (〖3x〗^2 - 3x - xy + y)/(〖9x〗^2 - y^2 ) = (3x(x - 1) - y(x - 1))/((3x - y)(3x + y)) = ((3x - y)(x - 1))/((3x - y)(3x + y)) = (x - 1)/(3x + y).
2) (a - 5)/〖ab - a〗^2 – (5 - b)/〖ab - b〗^2 = (a - 5)/(a(b - a)) – (5 - b)/(b(a - b)) = 〖5 - a〗^(\b)/(a(a - b)) – 〖5 - b〗^(\a)/(b(a- b)) = (5b - ab - 5a + ab)/(ab(a - b)) = (5b - 5a)/(ab(a - b)) = (-5(a - b))/(ab(a - b)) = –5/ab;
3) (x^2 + x - 2)/(x^2 - 4) – 2/(3x - 6) – 1 = (x^2 + x - 2)/((x - 2)(x + 2)) – 2^(\x+2)/(3(x - 2)) – 1^(\3(x^2-4)) = (〖3x〗^2 + 3x - 6 - 2x - 4 - 〖3x〗^2 + 12)/(3(x - 2)(x + 2)) = (x + 2)/(3(x- 2)(x + 2)) = 1/(3(x - 2)) = 1/(3x - 6);
4) (m^2 - 9)/(a^2 + 6a + 9) : (12 - 4m)/(ap + 3p) = ((m - 3)(m + 3))/〖(a + 3)〗^2 • (p(a + 3))/(4(3 - m)) = –((m - 3)(m + 3) • p)/((a + 3) • 4(m - 3)) = –(p(m + 3))/(4(a + 3)).