75. Представьте в виде дроби: a) $$\frac{x}{2} + \frac{y}{3}$$; в) $$\frac{a}{b} - \frac{b^2}{a}$$; б) $$\frac{c}{4} - \frac{d}{12}$$; г) $$\frac{3}{2x} - \frac{2}{3x}$$; д) $$\frac{5x}{8y} + \frac{x}{4y}$$; ж) $$\frac{1}{5a} - \frac{8}{25a}$$; e) $$\frac{17y}{24c} - \frac{25y}{36c}$$; з) $$\frac{3b}{4c} + \frac{c}{2b}$$; 76. Выполните действие: a) $$\frac{5y-3}{6y} + \frac{y+2}{4y}$$; в) $$\frac{b+2}{15b} - \frac{3c-5}{45c}$$; б) $$\frac{3x+5}{35x} + \frac{x-3}{21x}$$; г) $$\frac{8b+y}{40b} - \frac{6y+b}{30y}$$. 77. Преобразуйте в дробь выражение: a) $$\frac{15a-b}{12a} - \frac{a-4b}{9a}$$; б) $$\frac{7x+4}{8y} - \frac{3x-1}{6y}$$. 78. Выполните действие: a) $$\frac{b}{a^2} - \frac{1}{a}$$; в) $$\frac{1}{2a^7} + \frac{4-2a^3}{a^{10}}$$; б) $$\frac{1-x}{x^3} + \frac{1}{x^2}$$; г) $$\frac{a+b}{a^2} + \frac{a-b}{ab}$$; д) $$\frac{2a-3b}{a^2b} - \frac{4a-5b}{ab^2}$$; e) $$\frac{x-2y}{xy^2} - \frac{2y-x}{x^2y}$$;

Решения: 75. а) $$\frac{x}{2} + \frac{y}{3} = \frac{3x}{6} + \frac{2y}{6} = \frac{3x + 2y}{6}$$ в) $$\frac{a}{b} - \frac{b^2}{a} = \frac{a^2}{ab} - \frac{b^3}{ab} = \frac{a^2 - b^3}{ab}$$ б) $$\frac{c}{4} - \frac{d}{12} = \frac{3c}{12} - \frac{d}{12} = \frac{3c - d}{12}$$ г) $$\frac{3}{2x} - \frac{2}{3x} = \frac{9}{6x} - \frac{4}{6x} = \frac{5}{6x}$$ д) $$\frac{5x}{8y} + \frac{x}{4y} = \frac{5x}{8y} + \frac{2x}{8y} = \frac{7x}{8y}$$ ж) $$\frac{1}{5a} - \frac{8}{25a} = \frac{5}{25a} - \frac{8}{25a} = -\frac{3}{25a}$$ е) $$\frac{17y}{24c} - \frac{25y}{36c} = \frac{51y}{72c} - \frac{50y}{72c} = \frac{y}{72c}$$ з) $$\frac{3b}{4c} + \frac{c}{2b} = \frac{3b^2}{4bc} + \frac{2c^2}{4bc} = \frac{3b^2 + 2c^2}{4bc}$$ 76. а) $$\frac{5y-3}{6y} + \frac{y+2}{4y} = \frac{2(5y-3)}{12y} + \frac{3(y+2)}{12y} = \frac{10y - 6 + 3y + 6}{12y} = \frac{13y}{12y} = \frac{13}{12}$$ в) $$\frac{b+2}{15b} - \frac{3c-5}{45c} = \frac{3c(b+2)}{45bc} - \frac{b(3c-5)}{45bc} = \frac{3bc + 6c - 3bc + 5b}{45bc} = \frac{6c + 5b}{45bc}$$ б) $$\frac{3x+5}{35x} + \frac{x-3}{21x} = \frac{3(3x+5)}{105x} + \frac{5(x-3)}{105x} = \frac{9x + 15 + 5x - 15}{105x} = \frac{14x}{105x} = \frac{2}{15}$$ г) $$\frac{8b+y}{40b} - \frac{6y+b}{30y} = \frac{3y(8b+y)}{120by} - \frac{4b(6y+b)}{120by} = \frac{24by + 3y^2 - 24by - 4b^2}{120by} = \frac{3y^2 - 4b^2}{120by}$$ 77. а) $$\frac{15a-b}{12a} - \frac{a-4b}{9a} = \frac{3(15a-b)}{36a} - \frac{4(a-4b)}{36a} = \frac{45a - 3b - 4a + 16b}{36a} = \frac{41a + 13b}{36a}$$ б) $$\frac{7x+4}{8y} - \frac{3x-1}{6y} = \frac{3(7x+4)}{24y} - \frac{4(3x-1)}{24y} = \frac{21x + 12 - 12x + 4}{24y} = \frac{9x + 16}{24y}$$ 78. а) $$\frac{b}{a^2} - \frac{1}{a} = \frac{b}{a^2} - \frac{a}{a^2} = \frac{b-a}{a^2}$$ в) $$\frac{1}{2a^7} + \frac{4-2a^3}{a^{10}} = \frac{a^3}{2a^{10}} + \frac{2(4-2a^3)}{2a^{10}} = \frac{a^3 + 8 - 4a^3}{2a^{10}} = \frac{8-3a^3}{2a^{10}}$$ б) $$\frac{1-x}{x^3} + \frac{1}{x^2} = \frac{1-x}{x^3} + \frac{x}{x^3} = \frac{1-x+x}{x^3} = \frac{1}{x^3}$$ г) $$\frac{a+b}{a^2} + \frac{a-b}{ab} = \frac{b(a+b)}{a^2b} + \frac{a(a-b)}{a^2b} = \frac{ab + b^2 + a^2 - ab}{a^2b} = \frac{a^2 + b^2}{a^2b}$$ д) $$\frac{2a-3b}{a^2b} - \frac{4a-5b}{ab^2} = \frac{b(2a-3b)}{a^2b^2} - \frac{a(4a-5b)}{a^2b^2} = \frac{2ab - 3b^2 - 4a^2 + 5ab}{a^2b^2} = \frac{7ab - 3b^2 - 4a^2}{a^2b^2}$$ е) $$\frac{x-2y}{xy^2} - \frac{2y-x}{x^2y} = \frac{x(x-2y)}{x^2y^2} - \frac{y(2y-x)}{x^2y^2} = \frac{x^2 - 2xy - 2y^2 + xy}{x^2y^2} = \frac{x^2 - xy - 2y^2}{x^2y^2}$$