Выполни вычитание дробей с 51 по 74

51. $\frac{a^2}{a^2 - 1} - \frac{a}{a + 1} = \frac{a^2}{(a - 1)(a + 1)} - \frac{a}{a + 1} = \frac{a^2 - a(a - 1)}{(a - 1)(a + 1)} = \frac{a^2 - a^2 + a}{(a - 1)(a + 1)} = \frac{a}{a^2 - 1}$ 52. $\frac{c^2}{c^2 - 4} - \frac{c}{c - 2} = \frac{c^2}{(c - 2)(c + 2)} - \frac{c}{c - 2} = \frac{c^2 - c(c + 2)}{(c - 2)(c + 2)} = \frac{c^2 - c^2 - 2c}{(c - 2)(c + 2)} = \frac{-2c}{c^2 - 4}$ 53. $\frac{a^2 + b^2}{a^2 - b^2} - \frac{a - b}{a + b} = \frac{a^2 + b^2}{(a - b)(a + b)} - \frac{a - b}{a + b} = \frac{a^2 + b^2 - (a - b)^2}{(a - b)(a + b)} = \frac{a^2 + b^2 - (a^2 - 2ab + b^2)}{(a - b)(a + b)} = \frac{2ab}{a^2 - b^2}$ 54. $\frac{a^2 + b^2}{a^2 - b^2} - \frac{a + b}{a - b} = \frac{a^2 + b^2}{(a - b)(a + b)} - \frac{a + b}{a - b} = \frac{a^2 + b^2 - (a + b)^2}{(a - b)(a + b)} = \frac{a^2 + b^2 - (a^2 + 2ab + b^2)}{(a - b)(a + b)} = \frac{-2ab}{a^2 - b^2}$ 55. $\frac{a - b}{a + b} - \frac{a + b}{a - b} = \frac{(a - b)^2 - (a + b)^2}{(a + b)(a - b)} = \frac{(a^2 - 2ab + b^2) - (a^2 + 2ab + b^2)}{(a + b)(a - b)} = \frac{-4ab}{a^2 - b^2}$ 56. $\frac{m + n}{m - n} - \frac{m - n}{m + n} = \frac{(m + n)^2 - (m - n)^2}{(m - n)(m + n)} = \frac{(m^2 + 2mn + n^2) - (m^2 - 2mn + n^2)}{m^2 - n^2} = \frac{4mn}{m^2 - n^2}$ 57. $\frac{4x}{x^2 - y^2} - \frac{4}{x + y} = \frac{4x}{(x - y)(x + y)} - \frac{4}{x + y} = \frac{4x - 4(x - y)}{(x - y)(x + y)} = \frac{4x - 4x + 4y}{x^2 - y^2} = \frac{4y}{x^2 - y^2}$ 58. $\frac{3c}{a^2 - c^2} - \frac{2}{a - c} = \frac{3c}{(a - c)(a + c)} - \frac{2}{a - c} = \frac{3c - 2(a + c)}{(a - c)(a + c)} = \frac{3c - 2a - 2c}{a^2 - c^2} = \frac{c - 2a}{a^2 - c^2}$ 59. $\frac{a}{a - b} - \frac{a - b}{a + b} = \frac{a(a + b) - (a - b)^2}{(a - b)(a + b)} = \frac{a^2 + ab - (a^2 - 2ab + b^2)}{a^2 - b^2} = \frac{3ab - b^2}{a^2 - b^2}$ 60. $\frac{x - y}{x + y} - \frac{y}{x - y} = \frac{(x - y)^2 - y(x + y)}{(x + y)(x - y)} = \frac{x^2 - 2xy + y^2 - xy - y^2}{x^2 - y^2} = \frac{x^2 - 3xy}{x^2 - y^2}$ 61. $\frac{3b^2 + 2b}{b^2 - 4} - \frac{b}{b - 2} = \frac{3b^2 + 2b}{(b - 2)(b + 2)} - \frac{b}{b - 2} = \frac{3b^2 + 2b - b(b + 2)}{(b - 2)(b + 2)} = \frac{3b^2 + 2b - b^2 - 2b}{b^2 - 4} = \frac{2b^2}{b^2 - 4}$ 62. $\frac{3a^2 + 6a}{a^2 - 9} - \frac{2a}{a - 3} = \frac{3a^2 + 6a}{(a - 3)(a + 3)} - \frac{2a}{a - 3} = \frac{3a^2 + 6a - 2a(a + 3)}{(a - 3)(a + 3)} = \frac{3a^2 + 6a - 2a^2 - 6a}{a^2 - 9} = \frac{a^2}{a^2 - 9}$ 63. $\frac{20}{c^2 + 4c} - \frac{5}{c} = \frac{20}{c(c + 4)} - \frac{5}{c} = \frac{20 - 5(c + 4)}{c(c + 4)} = \frac{20 - 5c - 20}{c(c + 4)} = \frac{-5c}{c(c + 4)} = \frac{-5}{c + 4}$ 64. $\frac{9}{a^2 + 3a} - \frac{3}{a} = \frac{9}{a(a + 3)} - \frac{3}{a} = \frac{9 - 3(a + 3)}{a(a + 3)} = \frac{9 - 3a - 9}{a(a + 3)} = \frac{-3a}{a(a + 3)} = \frac{-3}{a + 3}$ 65. $\frac{a^2 + y^2}{ay - y^2} - \frac{20}{a - y} = \frac{a^2 + y^2}{y(a - y)} - \frac{20}{a - y} = \frac{a^2 + y^2 - 20y}{y(a - y)}$ 66. $\frac{a^2 + b^2}{2a^2 + 2ab} + \frac{b}{a + b} = \frac{a^2 + b^2}{2a(a + b)} + \frac{b}{a + b} = \frac{a^2 + b^2 + 2ab}{2a(a + b)} = \frac{(a + b)^2}{2a(a + b)} = \frac{a + b}{2a}$ 67. $\frac{4y}{y^2 - x^2} - \frac{2}{y - x} = \frac{4y}{(y - x)(y + x)} - \frac{2}{y - x} = \frac{4y - 2(y + x)}{(y - x)(y + x)} = \frac{4y - 2y - 2x}{y^2 - x^2} = \frac{2y - 2x}{y^2 - x^2} = \frac{2(y - x)}{(y - x)(y + x)} = \frac{2}{y + x}$ 68. $\frac{6a}{a^2 - b^2} - \frac{3}{a - b} = \frac{6a}{(a - b)(a + b)} - \frac{3}{a - b} = \frac{6a - 3(a + b)}{(a - b)(a + b)} = \frac{6a - 3a - 3b}{a^2 - b^2} = \frac{3a - 3b}{a^2 - b^2} = \frac{3(a - b)}{(a - b)(a + b)} = \frac{3}{a + b}$ 69. $\frac{b^2 + 4}{b^2 - 4} - \frac{b}{b + 2} = \frac{b^2 + 4}{(b - 2)(b + 2)} - \frac{b}{b + 2} = \frac{b^2 + 4 - b(b - 2)}{(b - 2)(b + 2)} = \frac{b^2 + 4 - b^2 + 2b}{b^2 - 4} = \frac{2b + 4}{b^2 - 4} = \frac{2(b + 2)}{(b - 2)(b + 2)} = \frac{2}{b - 2}$ 70. $\frac{a^2 + 9}{a^2 - 9} - \frac{a}{a + 3} = \frac{a^2 + 9}{(a - 3)(a + 3)} - \frac{a}{a + 3} = \frac{a^2 + 9 - a(a - 3)}{(a - 3)(a + 3)} = \frac{a^2 + 9 - a^2 + 3a}{a^2 - 9} = \frac{3a + 9}{a^2 - 9} = \frac{3(a + 3)}{(a - 3)(a + 3)} = \frac{3}{a - 3}$ 71. $\frac{2a}{a^2 - 9} - \frac{1}{a + 3} = \frac{2a}{(a - 3)(a + 3)} - \frac{1}{a + 3} = \frac{2a - (a - 3)}{(a - 3)(a + 3)} = \frac{2a - a + 3}{a^2 - 9} = \frac{a + 3}{a^2 - 9} = \frac{a + 3}{(a - 3)(a + 3)} = \frac{1}{a - 3}$ 72. $\frac{2a}{a^2 - 4} - \frac{1}{a - 2} = \frac{2a}{(a - 2)(a + 2)} - \frac{1}{a - 2} = \frac{2a - (a + 2)}{(a - 2)(a + 2)} = \frac{2a - a - 2}{a^2 - 4} = \frac{a - 2}{a^2 - 4} = \frac{a - 2}{(a - 2)(a + 2)} = \frac{1}{a + 2}$ 73. $\frac{a - c}{c} - \frac{a - c}{a + c} = \frac{(a - c)(a + c) - (a - c)c}{c(a + c)} = \frac{(a - c)(a + c - c)}{c(a + c)} = \frac{(a - c)a}{c(a + c)} = \frac{a^2 - ac}{c(a + c)}$ 74. $\frac{a + b}{a - b} - \frac{a + b}{a} = \frac{(a + b)a - (a + b)(a - b)}{a(a - b)} = \frac{(a + b)(a - (a - b))}{a(a - b)} = \frac{(a + b)b}{a(a - b)} = \frac{ab + b^2}{a(a - b)}$