Вычисли выражения 51-74

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