ГДЗ Алгебра 9 клас Істер НУШ

17. Виконайте дію:

1) (〖2a〗^2 - 2a)/(〖4a〗^2 - b^2 ) + (b(a - 1))/(b^2 - 〖4a〗^2 ) = (〖2a〗^2 - 2a)/(〖4a〗^2 - b^2 ) – (b(a - 1))/(〖4a〗^2 - b^2 ) = (2a(a - 1) - b(a - 1))/(〖4a〗^2 - b^2 ) = ((a - 1)(2a- b))/((2a - b)(2a + b)) = (a - 1)/(2a + b);
2) (x + 3)/(xy - x^2 ) + (y + 3)/(xy - y^2 ) = (x + 3)/(x(y - x)) + (y + 3)/(y(x - y)) = 〖x + 3〗^(\y)/(x(y - x)) – 〖y + 3〗^(\x)/(y(y - x)) = (xy + 3y - xy - 3x)/(xy(y - x)) = (-3(x - y))/(xy(y - x)) = (-3(x - y))/(-xy(x - y)) = 3/xy;
3) (x^2 + x - 3)/(x^2 - 9) – 3/(2x - 6) – 1 = (x^2 + x - 3^(\2))/((x - 3)(x + 3)) – 3^(\x + 3)/(2(x - 3)) 1^(\2(x^2-9)) = (〖2x〗^2 + 2x - 6 - 3x - 9 - 〖2x〗^2 + 18)/(2(x - 3)(x + 3)) = (-x + 3)/(2(x - 3)(x + 3)) = (-(x - 3))/(2(x - 3)(x + 3)) = –1/(2(x + 3));
4) (ax - 2x)/(3y + 6) : 〖4 - a〗^2/(y^2 - 4y + 4) = (x(a - 2))/(3(y + 2)) • 〖(y + 2)〗^2/((2 + a)(2 + a)) = –(x(a - 2)(y + 2))/(3(a - 2)(a + 2)) = –(x(y + 2))/(3(a + 2)).