1) а) 30x^3y / 45x^2y^2 = (15x^2y * 2x) / (15x^2y * 3y ) = 2x /3y
б) 5y / (y^2 - 2y) = 5y / (y *(y - 2)) = 5 / (y - 2)
в) (3a - 3b) / (a^2 - b^2) = (3 * (a - b)) / ((a - b) * (a + b)) = 3 / (a + b)
2) a) (3 - 2a) / 2a - (1 - a^2) / a^2 = a * (3 - 2a) / 2a^2 - 2 * (1 - a^2) / 2a^2 =
(3a - 2a^2 - 2 +2a^2) / 2a^2 = (3a - 2) / 2a^2
б) 1 / (3x + y) - 1 / (3x - y) = (3x - y) / (9x^2 - y^2) - (3x + y) / (9x^2 - y^2) = (3x - y - 3x - y) / (9x^2 - y^2) = - 2y / (9x^2 - y^2) = 2y / (y^2 - 9x^2)
в)
3) (x - 6y^2) / 2y + 3y = (x - 6y^2) / 2y + 3y * 2y / 2y = (x - 6y^2 + 6y^2) / 2y = x / 2y = (- 8) / 2 * 0.1 = - 8 / 0.2 = - 40
4) 2 / (x - 4) - (x + 8) / (x^2 - 16) - 1/ x = 2 / (x - 4) - (x + 8) / (x - 4)(x - 4) - 1 / x = 2 * x * (x + 4) / x * (x^2 - 16) - (x * (x + 8)) / x * (x^2 - 16) - (x^2 - 16) / x * (x^2 - 16) = (2x^2 + 8x - x^2 - 8x - x^2 + 16) / x * (x^2 - 16) = 16 / x * (x^2 - 16)