20. Представьте в виде дроби выражение: 1) \frac{6m}{26} + \frac{7m}{26}; 2) \frac{14a}{9b} - \frac{5a}{9b}; 3) \frac{4b - 15c}{18a} + \frac{2b + 3c}{18a}; 4) \frac{8m - 5n}{mn} - \frac{2m - 5n}{mn}; 5) \frac{2y}{y^2 - 49} - \frac{14}{y^2 - 49}; 6) \frac{x^2 + 12x}{25 - x^2} - \frac{2x - 25}{25 - x^2}. 21. Упростите выражение: 1) \frac{b - 6}{b - 3} - \frac{b}{3 - b}; 2) \frac{6c + 4}{7 - c} + \frac{3c + 25}{c - 7}; 3) \frac{(3a + 1)^2}{24a - 24} + \frac{(a + 3)^2}{24 - 24a}; 4) \frac{36 - 8x}{(x - 6)^2} - \frac{4x - x^2}{(6 - x)^2}. 24. Представьте в виде дроби выражение: 1) \frac{6}{x} + \frac{8}{y}; 2) \frac{2}{c} - \frac{7}{cd}; 3) \frac{9}{10mn} - \frac{14}{15mn}; 4) \frac{7a}{6m^2n} + \frac{9b}{4mn} - \frac{3c}{8mn^2}; 5) \frac{2x^2 - 4y^2}{xy} + \frac{6x + 4y}{x}; 6) \frac{4b^2 - 6b + 1}{ab^2} - \frac{b - 5}{ab}.

20. 1) \frac{6m}{26} + \frac{7m}{26} = \frac{6m + 7m}{26} = \frac{13m}{26} = \frac{m}{2} $$\frac{6m}{26} + \frac{7m}{26} = \frac{6m + 7m}{26} = \frac{13m}{26} = \frac{m}{2}$$ 2) \frac{14a}{9b} - \frac{5a}{9b} = \frac{14a - 5a}{9b} = \frac{9a}{9b} = \frac{a}{b} $$\frac{14a}{9b} - \frac{5a}{9b} = \frac{14a - 5a}{9b} = \frac{9a}{9b} = \frac{a}{b}$$ 3) \frac{4b - 15c}{18a} + \frac{2b + 3c}{18a} = \frac{4b - 15c + 2b + 3c}{18a} = \frac{6b - 12c}{18a} = \frac{6(b - 2c)}{18a} = \frac{b - 2c}{3a} $$\frac{4b - 15c}{18a} + \frac{2b + 3c}{18a} = \frac{4b - 15c + 2b + 3c}{18a} = \frac{6b - 12c}{18a} = \frac{6(b - 2c)}{18a} = \frac{b - 2c}{3a}$$ 4) \frac{8m - 5n}{mn} - \frac{2m - 5n}{mn} = \frac{8m - 5n - (2m - 5n)}{mn} = \frac{8m - 5n - 2m + 5n}{mn} = \frac{6m}{mn} = \frac{6}{n} $$\frac{8m - 5n}{mn} - \frac{2m - 5n}{mn} = \frac{8m - 5n - (2m - 5n)}{mn} = \frac{8m - 5n - 2m + 5n}{mn} = \frac{6m}{mn} = \frac{6}{n}$$ 5) \frac{2y}{y^2 - 49} - \frac{14}{y^2 - 49} = \frac{2y - 14}{y^2 - 49} = \frac{2(y - 7)}{(y - 7)(y + 7)} = \frac{2}{y + 7} $$\frac{2y}{y^2 - 49} - \frac{14}{y^2 - 49} = \frac{2y - 14}{y^2 - 49} = \frac{2(y - 7)}{(y - 7)(y + 7)} = \frac{2}{y + 7}$$ 6) \frac{x^2 + 12x}{25 - x^2} - \frac{2x - 25}{25 - x^2} = \frac{x^2 + 12x - (2x - 25)}{25 - x^2} = \frac{x^2 + 12x - 2x + 25}{25 - x^2} = \frac{x^2 + 10x + 25}{25 - x^2} = \frac{(x + 5)^2}{(5 - x)(5 + x)} = \frac{x + 5}{5 - x} $$\frac{x^2 + 12x}{25 - x^2} - \frac{2x - 25}{25 - x^2} = \frac{x^2 + 12x - (2x - 25)}{25 - x^2} = \frac{x^2 + 12x - 2x + 25}{25 - x^2} = \frac{x^2 + 10x + 25}{25 - x^2} = \frac{(x + 5)^2}{(5 - x)(5 + x)} = \frac{x + 5}{5 - x}$$ 21. 1) \frac{b - 6}{b - 3} - \frac{b}{3 - b} = \frac{b - 6}{b - 3} + \frac{b}{b - 3} = \frac{b - 6 + b}{b - 3} = \frac{2b - 6}{b - 3} = \frac{2(b - 3)}{b - 3} = 2 $$\frac{b - 6}{b - 3} - \frac{b}{3 - b} = \frac{b - 6}{b - 3} + \frac{b}{b - 3} = \frac{b - 6 + b}{b - 3} = \frac{2b - 6}{b - 3} = \frac{2(b - 3)}{b - 3} = 2$$ 2) \frac{6c + 4}{7 - c} + \frac{3c + 25}{c - 7} = \frac{6c + 4}{7 - c} - \frac{3c + 25}{7 - c} = \frac{6c + 4 - (3c + 25)}{7 - c} = \frac{6c + 4 - 3c - 25}{7 - c} = \frac{3c - 21}{7 - c} = \frac{3(c - 7)}{7 - c} = -3 $$\frac{6c + 4}{7 - c} + \frac{3c + 25}{c - 7} = \frac{6c + 4}{7 - c} - \frac{3c + 25}{7 - c} = \frac{6c + 4 - (3c + 25)}{7 - c} = \frac{6c + 4 - 3c - 25}{7 - c} = \frac{3c - 21}{7 - c} = \frac{3(c - 7)}{7 - c} = -3$$ 3) \frac{(3a + 1)^2}{24a - 24} + \frac{(a + 3)^2}{24 - 24a} = \frac{(3a + 1)^2}{24(a - 1)} - \frac{(a + 3)^2}{24(a - 1)} = \frac{(3a + 1)^2 - (a + 3)^2}{24(a - 1)} = \frac{(9a^2 + 6a + 1) - (a^2 + 6a + 9)}{24(a - 1)} = \frac{9a^2 + 6a + 1 - a^2 - 6a - 9}{24(a - 1)} = \frac{8a^2 - 8}{24(a - 1)} = \frac{8(a^2 - 1)}{24(a - 1)} = \frac{8(a - 1)(a + 1)}{24(a - 1)} = \frac{a + 1}{3} $$\frac{(3a + 1)^2}{24a - 24} + \frac{(a + 3)^2}{24 - 24a} = \frac{(3a + 1)^2}{24(a - 1)} - \frac{(a + 3)^2}{24(a - 1)} = \frac{(3a + 1)^2 - (a + 3)^2}{24(a - 1)} = \frac{(9a^2 + 6a + 1) - (a^2 + 6a + 9)}{24(a - 1)} = \frac{9a^2 + 6a + 1 - a^2 - 6a - 9}{24(a - 1)} = \frac{8a^2 - 8}{24(a - 1)} = \frac{8(a^2 - 1)}{24(a - 1)} = \frac{8(a - 1)(a + 1)}{24(a - 1)} = \frac{a + 1}{3}$$ 4) \frac{36 - 8x}{(x - 6)^2} - \frac{4x - x^2}{(6 - x)^2} = \frac{36 - 8x}{(x - 6)^2} - \frac{4x - x^2}{(x - 6)^2} = \frac{36 - 8x - (4x - x^2)}{(x - 6)^2} = \frac{36 - 8x - 4x + x^2}{(x - 6)^2} = \frac{x^2 - 12x + 36}{(x - 6)^2} = \frac{(x - 6)^2}{(x - 6)^2} = 1 $$\frac{36 - 8x}{(x - 6)^2} - \frac{4x - x^2}{(6 - x)^2} = \frac{36 - 8x}{(x - 6)^2} - \frac{4x - x^2}{(x - 6)^2} = \frac{36 - 8x - (4x - x^2)}{(x - 6)^2} = \frac{36 - 8x - 4x + x^2}{(x - 6)^2} = \frac{x^2 - 12x + 36}{(x - 6)^2} = \frac{(x - 6)^2}{(x - 6)^2} = 1$$ 24. 1) \frac{6}{x} + \frac{8}{y} = \frac{6y + 8x}{xy} $$\frac{6}{x} + \frac{8}{y} = \frac{6y + 8x}{xy}$$ 2) \frac{2}{c} - \frac{7}{cd} = \frac{2d - 7}{cd} $$\frac{2}{c} - \frac{7}{cd} = \frac{2d - 7}{cd}$$ 3) \frac{9}{10mn} - \frac{14}{15mn} = \frac{9 \cdot 3 - 14 \cdot 2}{30mn} = \frac{27 - 28}{30mn} = -\frac{1}{30mn} $$\frac{9}{10mn} - \frac{14}{15mn} = \frac{9 \cdot 3 - 14 \cdot 2}{30mn} = \frac{27 - 28}{30mn} = -\frac{1}{30mn}$$ 4) \frac{7a}{6m^2n} + \frac{9b}{4mn} - \frac{3c}{8mn^2} = \frac{7a \cdot 4n + 9b \cdot 6m^2 - 3c \cdot 3m}{24m^2n^2} = \frac{28an + 54bm^2 - 9cm}{24m^2n^2} $$\frac{7a}{6m^2n} + \frac{9b}{4mn} - \frac{3c}{8mn^2} = \frac{7a \cdot 4n + 9b \cdot 6m^2 - 3c \cdot 3m}{24m^2n^2} = \frac{28an + 54bm^2 - 9cm}{24m^2n^2}$$ 5) \frac{2x^2 - 4y^2}{xy} + \frac{6x + 4y}{x} = \frac{2x^2 - 4y^2 + (6x + 4y)y}{xy} = \frac{2x^2 - 4y^2 + 6xy + 4y^2}{xy} = \frac{2x^2 + 6xy}{xy} = \frac{2x(x + 3y)}{xy} = \frac{2(x + 3y)}{y} $$\frac{2x^2 - 4y^2}{xy} + \frac{6x + 4y}{x} = \frac{2x^2 - 4y^2 + (6x + 4y)y}{xy} = \frac{2x^2 - 4y^2 + 6xy + 4y^2}{xy} = \frac{2x^2 + 6xy}{xy} = \frac{2x(x + 3y)}{xy} = \frac{2(x + 3y)}{y}$$ 6) \frac{4b^2 - 6b + 1}{ab^2} - \frac{b - 5}{ab} = \frac{4b^2 - 6b + 1 - (b - 5)b}{ab^2} = \frac{4b^2 - 6b + 1 - b^2 + 5b}{ab^2} = \frac{3b^2 - b + 1}{ab^2} $$\frac{4b^2 - 6b + 1}{ab^2} - \frac{b - 5}{ab} = \frac{4b^2 - 6b + 1 - (b - 5)b}{ab^2} = \frac{4b^2 - 6b + 1 - b^2 + 5b}{ab^2} = \frac{3b^2 - b + 1}{ab^2}$$