Упрости выражения: 1) a² + b² / a²-b² - b / a+b + b / b-a; 2) x+7 / 3x+12 - 2/x + 7x+40 / 3x²+12x; 3) a-1 / 3a²+6a+3 - 1 / 2a+2; 4) y+6 / 4y+8 - y+2 / 4y-8 + 5 / y²-4; 5) a+3 / a²+3a+9 - 1 / a-3 + a³+3a-9 / a³-27.

Конечно, помогу! Давай упростим выражения по порядку: 1) $\frac{a^2 + b^2}{a^2 - b^2} - \frac{b}{a + b} + \frac{b}{b - a} = \frac{a^2 + b^2}{(a + b)(a - b)} - \frac{b}{a + b} - \frac{b}{a - b} = \frac{a^2 + b^2 - b(a - b) - b(a + b)}{(a + b)(a - b)} = \frac{a^2 + b^2 - ab + b^2 - ab - b^2}{(a + b)(a - b)} = \frac{a^2 - 2ab + b^2}{(a + b)(a - b)} = \frac{(a - b)^2}{(a + b)(a - b)} = \frac{a - b}{a + b}$ **Ответ: **$\frac{a - b}{a + b}$ 2) $\frac{x + 7}{3x + 12} - \frac{2}{x} + \frac{7x + 40}{3x^2 + 12x} = \frac{x + 7}{3(x + 4)} - \frac{2}{x} + \frac{7x + 40}{3x(x + 4)} = \frac{x(x + 7) - 2 \cdot 3(x + 4) + (7x + 40)}{3x(x + 4)} = \frac{x^2 + 7x - 6x - 24 + 7x + 40}{3x(x + 4)} = \frac{x^2 + 8x + 16}{3x(x + 4)} = \frac{(x + 4)^2}{3x(x + 4)} = \frac{x + 4}{3x}$ **Ответ: **$\frac{x + 4}{3x}$ 3) $\frac{a - 1}{3a^2 + 6a + 3} - \frac{1}{2a + 2} = \frac{a - 1}{3(a^2 + 2a + 1)} - \frac{1}{2(a + 1)} = \frac{a - 1}{3(a + 1)^2} - \frac{1}{2(a + 1)} = \frac{2(a - 1) - 3(a + 1)}{6(a + 1)^2} = \frac{2a - 2 - 3a - 3}{6(a + 1)^2} = \frac{-a - 5}{6(a + 1)^2} = -\frac{a + 5}{6(a + 1)^2}$ **Ответ: **$-\frac{a + 5}{6(a + 1)^2}$ 4) $\frac{y + 6}{4y + 8} - \frac{y + 2}{4y - 8} + \frac{5}{y^2 - 4} = \frac{y + 6}{4(y + 2)} - \frac{y + 2}{4(y - 2)} + \frac{5}{(y - 2)(y + 2)} = \frac{(y + 6)(y - 2) - (y + 2)^2 + 4 \cdot 5}{4(y - 2)(y + 2)} = \frac{y^2 + 4y - 12 - (y^2 + 4y + 4) + 20}{4(y - 2)(y + 2)} = \frac{y^2 + 4y - 12 - y^2 - 4y - 4 + 20}{4(y - 2)(y + 2)} = \frac{4}{4(y - 2)(y + 2)} = \frac{1}{(y - 2)(y + 2)} = \frac{1}{y^2 - 4}$ **Ответ: **$\frac{1}{y^2 - 4}$ 5) $\frac{a + 3}{a^2 + 3a + 9} - \frac{1}{a - 3} + \frac{a^3 + 3a - 9}{a^3 - 27} = \frac{a + 3}{a^2 + 3a + 9} - \frac{1}{a - 3} + \frac{a^3 + 3a - 9}{(a - 3)(a^2 + 3a + 9)} = \frac{(a + 3)(a - 3) - (a^2 + 3a + 9) + (a^3 + 3a - 9)}{(a - 3)(a^2 + 3a + 9)} = \frac{a^2 - 9 - a^2 - 3a - 9 + a^3 + 3a - 9}{(a - 3)(a^2 + 3a + 9)} = \frac{a^3 - 27}{(a - 3)(a^2 + 3a + 9)} = \frac{(a - 3)(a^2 + 3a + 9)}{(a - 3)(a^2 + 3a + 9)} = 1$ **Ответ: 1**