Представьте в виде дроби выражение: 1) $$\frac{4}{a} + \frac{7}{b}$$: 2) $$\frac{9}{m} - \frac{5}{mn}$$: 3) $$\frac{4}{12xy} - \frac{11}{18xy}$$: Выполните действия: 1) $$\frac{x-3}{3x+6} - \frac{x-6}{x+2}$$: 2) $$\frac{m+4}{5m-10} + \frac{3-m}{4m-8}$$: 3) $$\frac{y+6}{y-6} - \frac{y+2}{y+6}$$: 4) $$\frac{5m}{3ab} + \frac{2n}{5a^2b} - \frac{7p}{2ab^2}$$: 5) $$\frac{3a-4b}{a} + \frac{8a^2+4b^2}{ab}$$: 6) $$\frac{3c^2-2c+4}{bc^2} - \frac{2c-9}{bc}$$: 4) $$\frac{3x}{4x-4} + \frac{5x}{7-7x}$$: 5) $$\frac{2b}{2b+c} - \frac{4b^2}{4b^2+4bc+c^2}$$: 6) $$\frac{2}{a^2-9} - \frac{1}{a^2+3a}$$:

Решим представленные выражения и выполним действия: 1) $$\frac{4}{a} + \frac{7}{b} = \frac{4b + 7a}{ab}$$ 2) $$\frac{9}{m} - \frac{5}{mn} = \frac{9n - 5}{mn}$$ 3) $$\frac{4}{12xy} - \frac{11}{18xy} = \frac{1}{3xy} - \frac{11}{18xy} = \frac{6 - 11}{18xy} = \frac{-5}{18xy}$$ Выполните действия: 1) $$\frac{x-3}{3x+6} - \frac{x-6}{x+2} = \frac{x-3}{3(x+2)} - \frac{x-6}{x+2} = \frac{(x-3) - 3(x-6)}{3(x+2)} = \frac{x - 3 - 3x + 18}{3(x+2)} = \frac{-2x + 15}{3(x+2)}$$ 2) $$\frac{m+4}{5m-10} + \frac{3-m}{4m-8} = \frac{m+4}{5(m-2)} + \frac{3-m}{4(m-2)} = \frac{4(m+4) + 5(3-m)}{20(m-2)} = \frac{4m + 16 + 15 - 5m}{20(m-2)} = \frac{-m + 31}{20(m-2)}$$ 3) $$\frac{y+6}{y-6} - \frac{y+2}{y+6} = \frac{(y+6)^2 - (y+2)(y-6)}{(y-6)(y+6)} = \frac{y^2 + 12y + 36 - (y^2 - 6y + 2y - 12)}{y^2 - 36} = \frac{y^2 + 12y + 36 - y^2 + 4y + 12}{y^2 - 36} = \frac{16y + 48}{y^2 - 36} = \frac{16(y+3)}{(y-6)(y+6)}$$ 4) $$\frac{5m}{3ab} + \frac{2n}{5a^2b} - \frac{7p}{2ab^2} = \frac{50a b m + 12b n - 105 a p}{30a^2b^2}$$ 5) $$\frac{3a-4b}{a} + \frac{8a^2+4b^2}{ab} = \frac{b(3a-4b) + 8a^2 + 4b^2}{ab} = \frac{3ab - 4b^2 + 8a^2 + 4b^2}{ab} = \frac{3ab + 8a^2}{ab} = \frac{a(3b + 8a)}{ab} = \frac{3b + 8a}{b}$$ 6) $$\frac{3c^2-2c+4}{bc^2} - \frac{2c-9}{bc} = \frac{3c^2 - 2c + 4 - c(2c - 9)}{bc^2} = \frac{3c^2 - 2c + 4 - 2c^2 + 9c}{bc^2} = \frac{c^2 + 7c + 4}{bc^2}$$ 4) $$\frac{3x}{4x-4} + \frac{5x}{7-7x} = \frac{3x}{4(x-1)} - \frac{5x}{7(x-1)} = \frac{21x - 20x}{28(x-1)} = \frac{x}{28(x-1)}$$ 5) $$\frac{2b}{2b+c} - \frac{4b^2}{4b^2+4bc+c^2} = \frac{2b(2b+c) - 4b^2}{(2b+c)^2} = \frac{4b^2 + 2bc - 4b^2}{(2b+c)^2} = \frac{2bc}{(2b+c)^2}$$ 6) $$\frac{2}{a^2-9} - \frac{1}{a^2+3a} = \frac{2}{(a-3)(a+3)} - \frac{1}{a(a+3)} = \frac{2a - (a-3)}{a(a-3)(a+3)} = \frac{a + 3}{a(a-3)(a+3)} = \frac{1}{a(a-3)}$$