Реши примеры с 63 по 74 на упрощение алгебраических дробей.

63. $\frac{20}{c^2 + 4c} - \frac{5}{c} = \frac{20}{c(c + 4)} - \frac{5}{c} = \frac{20 - 5(c + 4)}{c(c + 4)} = \frac{20 - 5c - 20}{c(c + 4)} = \frac{-5c}{c(c + 4)} = \frac{-5}{c + 4}$ **Ответ: $\frac{-5}{c + 4}$** 64. $\frac{9}{a^2 + 3a} - \frac{3}{a} = \frac{9}{a(a + 3)} - \frac{3}{a} = \frac{9 - 3(a + 3)}{a(a + 3)} = \frac{9 - 3a - 9}{a(a + 3)} = \frac{-3a}{a(a + 3)} = \frac{-3}{a + 3}$ **Ответ: $\frac{-3}{a + 3}$** 65. $\frac{a^2 + y^2}{ay - y^2} - \frac{20}{a - y} = \frac{a^2 + y^2}{y(a - y)} - \frac{20}{a - y} = \frac{a^2 + y^2 - 20y}{y(a - y)}$ **Ответ: $\frac{a^2 + y^2 - 20y}{y(a - y)}$** 66. $\frac{a^2 + b^2}{2a^2 + 2ab} + \frac{b}{a + b} = \frac{a^2 + b^2}{2a(a + b)} + \frac{b}{a + b} = \frac{a^2 + b^2 + 2ab}{2a(a + b)} = \frac{(a + b)^2}{2a(a + b)} = \frac{a + b}{2a}$ **Ответ: $\frac{a + b}{2a}$** 67. $\frac{4y}{y^2 - x^2} - \frac{2}{y - x} = \frac{4y}{(y - x)(y + x)} - \frac{2}{y - x} = \frac{4y - 2(y + x)}{(y - x)(y + x)} = \frac{4y - 2y - 2x}{(y - x)(y + x)} = \frac{2y - 2x}{(y - x)(y + x)} = \frac{2(y - x)}{(y - x)(y + x)} = \frac{2}{y + x}$ **Ответ: $\frac{2}{y + x}$** 68. $\frac{6a}{a^2 - b^2} - \frac{3}{a - b} = \frac{6a}{(a - b)(a + b)} - \frac{3}{a - b} = \frac{6a - 3(a + b)}{(a - b)(a + b)} = \frac{6a - 3a - 3b}{(a - b)(a + b)} = \frac{3a - 3b}{(a - b)(a + b)} = \frac{3(a - b)}{(a - b)(a + b)} = \frac{3}{a + b}$ **Ответ: $\frac{3}{a + b}$** 69. $\frac{b^2 + 4}{b^2 - 4} - \frac{b}{b + 2} = \frac{b^2 + 4}{(b - 2)(b + 2)} - \frac{b}{b + 2} = \frac{b^2 + 4 - b(b - 2)}{(b - 2)(b + 2)} = \frac{b^2 + 4 - b^2 + 2b}{(b - 2)(b + 2)} = \frac{2b + 4}{(b - 2)(b + 2)} = \frac{2(b + 2)}{(b - 2)(b + 2)} = \frac{2}{b - 2}$ **Ответ: $\frac{2}{b - 2}$** 70. $\frac{a^2 + 9}{a^2 - 9} - \frac{a}{a + 3} = \frac{a^2 + 9}{(a - 3)(a + 3)} - \frac{a}{a + 3} = \frac{a^2 + 9 - a(a - 3)}{(a - 3)(a + 3)} = \frac{a^2 + 9 - a^2 + 3a}{(a - 3)(a + 3)} = \frac{3a + 9}{(a - 3)(a + 3)} = \frac{3(a + 3)}{(a - 3)(a + 3)} = \frac{3}{a - 3}$ **Ответ: $\frac{3}{a - 3}$** 71. $\frac{2a}{a^2 - 9} - \frac{1}{a + 3} = \frac{2a}{(a - 3)(a + 3)} - \frac{1}{a + 3} = \frac{2a - (a - 3)}{(a - 3)(a + 3)} = \frac{2a - a + 3}{(a - 3)(a + 3)} = \frac{a + 3}{(a - 3)(a + 3)} = \frac{1}{a - 3}$ **Ответ: $\frac{1}{a - 3}$** 72. $\frac{2a}{a^2 - 4} - \frac{1}{a - 2} = \frac{2a}{(a - 2)(a + 2)} - \frac{1}{a - 2} = \frac{2a - (a + 2)}{(a - 2)(a + 2)} = \frac{2a - a - 2}{(a - 2)(a + 2)} = \frac{a - 2}{(a - 2)(a + 2)} = \frac{1}{a + 2}$ **Ответ: $\frac{1}{a + 2}$** 73. $\frac{a - c}{c} - \frac{a - c}{a + c} = \frac{(a - c)(a + c) - c(a - c)}{c(a + c)} = \frac{a^2 - c^2 - ac + c^2}{c(a + c)} = \frac{a^2 - ac}{c(a + c)} = \frac{a(a - c)}{c(a + c)}$ **Ответ: $\frac{a(a - c)}{c(a + c)}$** 74. $\frac{a + b}{a - b} - \frac{a + b}{a} = \frac{a(a + b) - (a + b)(a - b)}{a(a - b)} = \frac{a^2 + ab - (a^2 - b^2)}{a(a - b)} = \frac{a^2 + ab - a^2 + b^2}{a(a - b)} = \frac{ab + b^2}{a(a - b)} = \frac{b(a + b)}{a(a - b)}$ **Ответ: $\frac{b(a + b)}{a(a - b)}$**