Решение:

a)

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

Ответ: $$ \frac{-16}{a^2-9} $$

б)

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

Ответ: $$ \frac{6x-1}{4x^2-1} $$

в)

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

Ответ: $$ \frac{-c}{a} $$

г)

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

Ответ: $$ \frac{2(y+a)}{a(x-3)} $$