152. Выполните действия: a) $$\frac{a^2 - 25}{a + 3} \cdot \frac{1}{a^2 + 5a} - \frac{a + 5}{a^2 - 3a}$$; б) $$\frac{1 - 2x}{2x + 1} + \frac{x^2 + 3x}{4x^2 - 1} : \frac{3 + x}{4x + 2}$$; в) $$\frac{b - c}{a + b} - \frac{ab - b^2}{a^2 - ac} \cdot \frac{a^2}{a^2 - b^2}$$; г) $$\frac{a^2 - 4}{x^2 - 9} : \frac{a^2 - 2a}{xy + 3y} + \frac{2 - y}{x - 3}$$.

a)$$\frac{a^2 - 25}{a + 3} \cdot \frac{1}{a^2 + 5a} - \frac{a + 5}{a^2 - 3a} = \frac{(a - 5)(a + 5)}{(a + 3)} \cdot \frac{1}{a(a + 5)} - \frac{a + 5}{a(a - 3)} = \frac{a - 5}{a(a + 3)} - \frac{a + 5}{a(a - 3)} = \frac{(a - 5)(a - 3) - (a + 5)(a + 3)}{a(a + 3)(a - 3)} = \frac{a^2 - 8a + 15 - (a^2 + 8a + 15)}{a(a^2 - 9)} = \frac{-16a}{a(a^2 - 9)} = \frac{-16}{a^2 - 9}$$

б)$$\frac{1 - 2x}{2x + 1} + \frac{x^2 + 3x}{4x^2 - 1} : \frac{3 + x}{4x + 2} = \frac{1 - 2x}{2x + 1} + \frac{x(x + 3)}{(2x - 1)(2x + 1)} \cdot \frac{2(2x + 1)}{x + 3} = \frac{1 - 2x}{2x + 1} + \frac{2x}{2x - 1} = \frac{(1 - 2x)(2x - 1) + 2x(2x + 1)}{(2x + 1)(2x - 1)} = \frac{2x - 1 - 4x^2 + 2x + 4x^2 + 2x}{4x^2 - 1} = \frac{6x - 1}{4x^2 - 1}$$

в)$$\frac{b - c}{a + b} - \frac{ab - b^2}{a^2 - ac} \cdot \frac{a^2}{a^2 - b^2} = \frac{b - c}{a + b} - \frac{b(a - b)}{a(a - c)} \cdot \frac{a^2}{(a - b)(a + b)} = \frac{b - c}{a + b} - \frac{ab}{a - c} \cdot \frac{1}{a + b} = \frac{(b - c)(a - c) - ab}{(a + b)(a - c)} = \frac{ab - bc - ac + c^2 - ab}{(a + b)(a - c)} = \frac{-bc - ac + c^2}{(a + b)(a - c)} = \frac{c^2 - ac - bc}{(a + b)(a - c)}$$

г)$$\frac{a^2 - 4}{x^2 - 9} : \frac{a^2 - 2a}{xy + 3y} + \frac{2 - y}{x - 3} = \frac{(a - 2)(a + 2)}{(x - 3)(x + 3)} : \frac{a(a - 2)}{y(x + 3)} + \frac{2 - y}{x - 3} = \frac{(a + 2)(a - 2)}{(x - 3)(x + 3)} \cdot \frac{y(x + 3)}{a(a - 2)} + \frac{2 - y}{x - 3} = \frac{y(a + 2)}{a(x - 3)} + \frac{2 - y}{x - 3} = \frac{y(a + 2) + a(2 - y)}{a(x - 3)} = \frac{ay + 2y + 2a - ay}{a(x - 3)} = \frac{2y + 2a}{a(x - 3)} = \frac{2(y + a)}{a(x - 3)}$$