Реши примеры с 51 по 62

Конечно, давай решим эти примеры. Вот ответы: 51. $\frac{a^2}{a^2-1} - \frac{a}{a+1} = \frac{a^2 - a(a-1)}{a^2-1} = \frac{a^2 - a^2 + a}{a^2-1} = \frac{a}{a^2-1}$ 52. $\frac{c^2}{c^2-4} - \frac{c}{c-2} = \frac{c^2 - c(c+2)}{c^2-4} = \frac{c^2 - c^2 - 2c}{c^2-4} = \frac{-2c}{c^2-4}$ 53. $\frac{a^2+b^2}{a^2-b^2} - \frac{a-b}{a+b} = \frac{a^2+b^2 - (a-b)(a-b)}{a^2-b^2} = \frac{a^2+b^2 - (a^2 - 2ab + b^2)}{a^2-b^2} = \frac{2ab}{a^2-b^2}$ 54. $\frac{a^2+b^2}{a^2-b^2} - \frac{a+b}{a-b} = \frac{a^2+b^2 - (a+b)(a+b)}{a^2-b^2} = \frac{a^2+b^2 - (a^2 + 2ab + b^2)}{a^2-b^2} = \frac{-2ab}{a^2-b^2}$ 55. $\frac{a-b}{a+b} - \frac{a+b}{a-b} = \frac{(a-b)(a-b) - (a+b)(a+b)}{(a+b)(a-b)} = \frac{(a^2 - 2ab + b^2) - (a^2 + 2ab + b^2)}{a^2-b^2} = \frac{-4ab}{a^2-b^2}$ 56. $\frac{m+n}{m-n} - \frac{m-n}{m+n} = \frac{(m+n)(m+n) - (m-n)(m-n)}{(m-n)(m+n)} = \frac{(m^2 + 2mn + n^2) - (m^2 - 2mn + n^2)}{m^2-n^2} = \frac{4mn}{m^2-n^2}$ 57. $\frac{4x}{x^2-y^2} - \frac{4}{x+y} = \frac{4x - 4(x-y)}{x^2-y^2} = \frac{4x - 4x + 4y}{x^2-y^2} = \frac{4y}{x^2-y^2}$ 58. $\frac{3c}{a^2-c^2} - \frac{2}{a-c} = \frac{3c - 2(a+c)}{a^2-c^2} = \frac{3c - 2a - 2c}{a^2-c^2} = \frac{c - 2a}{a^2-c^2}$ 59. $\frac{a}{a-b} - \frac{a-b}{a+b} = \frac{a(a+b) - (a-b)(a-b)}{(a-b)(a+b)} = \frac{a^2 + ab - (a^2 - 2ab + b^2)}{a^2-b^2} = \frac{3ab - b^2}{a^2-b^2}$ 60. $\frac{x-y}{x+y} - \frac{y}{x-y} = \frac{(x-y)(x-y) - y(x+y)}{(x+y)(x-y)} = \frac{x^2 - 2xy + y^2 - xy - y^2}{x^2-y^2} = \frac{x^2 - 3xy}{x^2-y^2}$ 61. $\frac{3b^2+2b}{b^2-4} - \frac{b}{b-2} = \frac{3b^2+2b - b(b+2)}{b^2-4} = \frac{3b^2+2b - b^2 - 2b}{b^2-4} = \frac{2b^2}{b^2-4}$ 62. $\frac{3a^2+6a}{a^2-9} - \frac{2a}{a-3} = \frac{3a^2+6a - 2a(a+3)}{a^2-9} = \frac{3a^2+6a - 2a^2 - 6a}{a^2-9} = \frac{a^2}{a^2-9}$