Выполните сложение и вычитание алгебраических дробей: a) b+3a/18a^2b + a-4b/24ab^2 b) m-4/m - m-3/m+1 c) y+3/4y (y-3) - y-3/4y (y+3) d) a-5/5a+25 + 3a+5/a^2+5a

a) (b + 3a) / 18a²b + (a - 4b) / 24ab² = ((b + 3a) * 4 * b + (a - 4b) * 3 * a) / 72a²b² = (4b² + 12ab + 3a² - 12ab) / 72a²b² = (4b² + 3a²) / 72a²b²;

b) (m - 4) / m - (m - 3) / (m + 1) = ((m - 4) * (m + 1) - m * (m - 3)) / m (m + 1) = (m² + m - 4m - 4 - m² + 3m) / m (m + 1) = - 4/m (m + 1);

c) (y + 3) / 4y (y - 3) - (y - 3) / 4y (y + 3) = ((y + 3) (y + 3) - (y - 3) (y - 3)) / 4y (y - 3) (y + 3) = ((y + 3) ² - (y - 3) ²) / 4y (y² - 9) = (y² + 6y + 9 - y² + 6y - 9) / 4y (y² - 9) = 12y/4y (y² - 9) = 3 / (y² - 9);

d) (a - 5) / (5a + 25) + (3a + 5) / (a² + 5a) = (a - 5) / 5 (a + 5) + (3a + 5) / a (a + 5) = (a (a - 5) + 5 (3a + 5)) / 5a (a + 5) = (a² - 5a + 15a + 25) / 5a (a + 5) = (a² + 10a + 25) / 5a (a + 5) = (a + 5) ²/5a (a + 5) = (a + 5) / 5a.