1) \(\frac{15-5y}{9-y^2}\) 2) \(\frac{m^2-4mn+4n^2}{m^2-4n^2}\) 3) \(\frac{4m^2n^5p}{12mn^5p}\) 4) \(\frac{184x-94}{27xy}\) 5) \(\frac{2x-3x^2y}{5xy}\) 6) \(\frac{x^2-9}{x-3}\) 7) \(\frac{x^2-4x+4}{x^2-4}\) 8) \(\frac{2x^2-18}{x-3}\)

Решение:

Давай разберем по порядку каждое выражение:

1. \(\frac{15-5y}{9-y^2}\) = \(\frac{5(3-y)}{(3-y)(3+y)}\) = \(\frac{5}{3+y}\)

2. \(\frac{m^2-4mn+4n^2}{m^2-4n^2}\) = \(\frac{(m-2n)^2}{(m-2n)(m+2n)}\) = \(\frac{m-2n}{m+2n}\)

3. \(\frac{4m^2n^5p}{12mn^5p}\) = \(\frac{m}{3}\)

4. \(\frac{184x-94}{27xy}\) = \(\frac{2(92x-47)}{27xy}\)

5. \(\frac{2x-3x^2y}{5xy}\) = \(\frac{x(2-3xy)}{5xy}\) = \(\frac{2-3xy}{5y}\)

6. \(\frac{x^2-9}{x-3}\) = \(\frac{(x-3)(x+3)}{x-3}\) = \(x+3\)

7. \(\frac{x^2-4x+4}{x^2-4}\) = \(\frac{(x-2)^2}{(x-2)(x+2)}\) = \(\frac{x-2}{x+2}\)

8. \(\frac{2x^2-18}{x-3}\) = \(\frac{2(x^2-9)}{x-3}\) = \(\frac{2(x-3)(x+3)}{x-3}\) = \(2(x+3)\)

Ответ: См. решение