2 1) a²-b²/3a+3b · 3a²/5b-5a ; 2) 5x²-5y²/x²+y² · 3x²/10y-10x ; 3) a²-25/a²-3a : a+5/9-a ; 4) 3n²-3m²/n²+np · 6m-6n/n+p ; 5) a²+b²/x³+x²y · x²-y²/a⁴-b⁴ ; 6) a²+b²/a²-ab : a⁴b-b⁵/a²b-ab² .

Решим каждое выражение пошагово:

1) $$\frac{a^2-b^2}{3a+3b} \cdot \frac{3a^2}{5b-5a} = \frac{(a-b)(a+b)}{3(a+b)} \cdot \frac{3a^2}{5(b-a)} = \frac{(a-b)3a^2}{3 \cdot 5 (b-a)} = -\frac{a^2}{5}$$

Ответ: $$\frac{-a^2}{5}$$

2) $$\frac{5x^2-5y^2}{x^2+y^2} \cdot \frac{3x^2}{10y-10x} = \frac{5(x^2-y^2)}{x^2+y^2} \cdot \frac{3x^2}{10(y-x)} = \frac{5(x-y)(x+y)3x^2}{10(y-x)(x^2+y^2)} = -\frac{3x^2(x+y)}{2(x^2+y^2)}$$

Ответ: $$\frac{-3x^2(x+y)}{2(x^2+y^2)}$$

3) $$\frac{a^2-25}{a^2-3a} : \frac{a+5}{9-a} = \frac{(a-5)(a+5)}{a(a-3)} : \frac{a+5}{-(a-9)} = \frac{(a-5)(a+5)}{a(a-3)} \cdot \frac{-(a-9)}{a+5} = \frac{-(a-5)(a-9)}{a(a-3)}$$

Ответ: $$\frac{-(a-5)(a-9)}{a(a-3)}$$

4) $$\frac{3n^2-3m^2}{n^2+np} \cdot \frac{6m-6n}{n+p} = \frac{3(n^2-m^2)}{n(n+p)} \cdot \frac{6(m-n)}{n+p} = \frac{3(n-m)(n+m)6(m-n)}{n(n+p)^2} = \frac{-18(n-m)^2(n+m)}{n(n+p)^2}$$

Ответ: $$\frac{-18(n-m)^2(n+m)}{n(n+p)^2}$$

5) $$\frac{a^2+b^2}{x^3+x^2y} \cdot \frac{x^2-y^2}{a^4-b^4} = \frac{a^2+b^2}{x^2(x+y)} \cdot \frac{(x-y)(x+y)}{(a^2-b^2)(a^2+b^2)} = \frac{(x-y)(x+y)}{x^2(x+y)(a^2-b^2)} = \frac{x-y}{x^2(a^2-b^2)}$$

Ответ: $$\frac{x-y}{x^2(a^2-b^2)}$$

6) $$\frac{a^2+b^2}{a^2-ab} : \frac{a^4b-b^5}{a^2b-ab^2} = \frac{a^2+b^2}{a(a-b)} : \frac{b(a^4-b^4)}{ab(a-b)} = \frac{a^2+b^2}{a(a-b)} \cdot \frac{ab(a-b)}{b(a^2-b^2)(a^2+b^2)} = \frac{ab}{ab(a^2-b^2)} = \frac{1}{a^2-b^2}$$

Ответ: $$\frac{1}{a^2-b^2}$$