1.
1. (2-b)/b + (b-3)/3b^2 = (3b(2-b) + b - 3) / 3b^2 = (6b - 3b^2 + b - 3) / 3b^2 = (-3b^2 + 7b - 3) / 3b^2
2. [(3c + 9) / 6c] * [2c^4 / (c + 3)] = [3(c+3) * 2c^4] / [6c * (c + 3)] = c^3
3. [(x^2 - y^2) / 6y] / (x - y)^2 = [(x-y)(x+y)] / [6y * (x-y)^2] = (x+y) / [6y * (x-y)]
2.
5/a - [(a / (4-a)) * ((16 - a^2) / a^2)] = 5/a - [a*(4-a)(4+a)] / [(4-a) * a^2] = 5/a - (4+a)/a = (1-a)/a
3.
(x^2 + 14xy + 49y^2)/(x^2 - 49y^2) * (21y - 3x) / (7x^2 + 49xy) = [(x^2 + 14xy + 49y^2) * (21y - 3x)] / [(x^2 - 49y^2) * (7x^2 + 49xy)] = [(x + 7y)^2 * 3(7y - x)] / [(x-7y)(x+7y) * 7x(x+7y)] = [переставляем местами члены в числителе и меняем знак дроби на противоположный, сокращаем возможное] = -3/(7x)
При x = 9:
-3 / 7*9 = -1 / 21
4.
[(2m/(m+4) + 16/(m^2-4m+16) - (m^3-20m^2)/(m^3+64)] * [(m + 4 - 12m/(m+4)] / (m+4) = [(2m/(m+4) + 16/(m^2-4m+16) - (m^3-20m^2)/[(m+4)*(m^2-4m+16)]] * [((m+4)^2 - 12m) / (m+4)^2] = [[(2m*(m^2-4m+16)) + 16(m+4) - (m^3-20m^2)] / (m^3+64)] * [((m+4)^2 - 12m) / (m+4)^2] = [(2m^3 - 8m^2 + 32m + 16m + 64 - m^3 + 20m^2) / (m^3 + 64)] * [(m^2 + 8m + 16 - 12m) / (m+4)^2] = [(m^3 + 12m^2 + 48m + 64) / (m^3 + 64)] * [(m^2 - 4m + 16) / (m+4)^2] = [[(m+4) * (m^2 + 8m + 16)] / [(m+4) * (m^2 - 4m + 16)]] * [(m-4)^2 / (m+4)^2] = [(m+4)^2 * (m-4)^2] / [(m^2 - 4m + 16) * (m+4)^2] = (m-4)^2 / (m^2 - 4m + 16)