№1. Сократите дроби : 1) 15/30 ; 2) 14/21 ; 3) 15-5y/9-y² ; 4) 36-12a+a²/a-6 №2. Выполните действия: 3x²/16-y² : 15x⁵/4+y x²-1/x²-4 * 5x+10/x+1 2/x-y + x-y/xy 8m-n/mn - m² - m-8n/mn - n² x-9/x²-9 - 3/3x - x²

Ответ:

№1. Сократите дроби:

1. \[\frac{15}{30} = \frac{1}{2}\]

2. \[\frac{14}{21} = \frac{2}{3}\]

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

4. \[\frac{36-12a+a^2}{a-6} = \frac{(a-6)^2}{a-6} = a-6\]

№2. Выполните действия:

1. \[\frac{3x^2}{16-y^2} : \frac{15x^5}{4+y} = \frac{3x^2}{(4-y)(4+y)} * \frac{4+y}{15x^5} = \frac{1}{5x^3(4-y)}\]

2. \[\frac{x^2-1}{x^2-4} * \frac{5x+10}{x+1} = \frac{(x-1)(x+1)}{(x-2)(x+2)} * \frac{5(x+2)}{x+1} = \frac{5(x-1)}{x-2}\]

3. \[\frac{2}{x-y} + \frac{x-y}{xy} = \frac{2xy + (x-y)^2}{xy(x-y)} = \frac{2xy + x^2 - 2xy + y^2}{xy(x-y)} = \frac{x^2 + y^2}{xy(x-y)}\]

4. \[\frac{8m-n}{mn-m^2} - \frac{m-8n}{mn-n^2} = \frac{8m-n}{m(n-m)} - \frac{m-8n}{n(m-n)} = \frac{n(8m-n) + m(m-8n)}{mn(m-n)} = \frac{8mn - n^2 + m^2 - 8mn}{mn(m-n)} = \frac{m^2 - n^2}{mn(m-n)} = \frac{(m-n)(m+n)}{mn(m-n)} = \frac{m+n}{mn}\]

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

Ответ: