8.21. Упростите выражение: 1) 4b/(a^2-b^2) + (a-b)/(a^2+ab) + (a+b)/(b^2-ab);

1) $\frac{4b}{(a-b)(a+b)} + \frac{a-b}{a(a+b)} - \frac{a+b}{b(a-b)} = \frac{4ab - (a-b)^2(b) - (a+b)^2(a)}{ab(a-b)(a+b)} = \frac{4ab - b(a^2-2ab+b^2) - a(a^2+2ab+b^2)}{ab(a^2-b^2)} = \frac{4ab - a^2b + 2ab^2 - b^3 - a^3 - 2a^2b - ab^2}{ab(a^2-b^2)} = \frac{-a^3 - 3a^2b + ab^2 - b^3}{ab(a^2-b^2)}$ 2) $\frac{1}{x-2} + \frac{1}{x+2} - \frac{x}{x^2-4} - \frac{x^2+4}{2x(x^2-4)} = \frac{2x}{x^2-4} - \frac{x}{x^2-4} - \frac{x^2+4}{2x(x^2-4)} = \frac{x}{x^2-4} - \frac{x^2+4}{2x(x^2-4)} = \frac{2x^2 - (x^2+4)}{2x(x^2-4)} = \frac{x^2-4}{2x(x^2-4)} = \frac{1}{2x}$ 3) $\frac{1}{(a-5b)^2} - \frac{2}{(a-5b)(a+5b)} + \frac{1}{(a+5b)^2} = \frac{(a+5b)^2 - 2(a^2-25b^2) + (a-5b)^2}{(a-5b)^2(a+5b)^2} = \frac{a^2+10ab+25b^2 - 2a^2 + 50b^2 + a^2-10ab+25b^2}{(a^2-25b^2)^2} = \frac{100b^2}{(a^2-25b^2)^2}$ 4) $\frac{x^2+9x+18}{y(x+3) - 2(x+3)} - \frac{x+5}{y-2} = \frac{(x+3)(x+6)}{(y-2)(x+3)} - \frac{x+5}{y-2} = \frac{x+6}{y-2} - \frac{x+5}{y-2} = \frac{1}{y-2}$