20. Среда. Проверь себя. Тема: «Сокращение дробей». Сократи дроби.

Сокращение дробей:

1. \( \frac{12a^8x^9}{4a^2x^{11}} = \frac{12}{4} \cdot \frac{a^8}{a^2} \cdot \frac{x^9}{x^{11}} = 3 \cdot a^{8-2} \cdot x^{9-11} = 3a^6x^{-2} = \frac{3a^6}{x^2} \)
2. \( \frac{x-y}{x^2-y^2} = \frac{x-y}{(x-y)(x+y)} = \frac{1}{x+y} \)
3. \( \frac{a^2-2ay+y^2}{a-y} = \frac{(a-y)^2}{a-y} = a-y \)
4. \( \frac{n^2-x^2}{n^2+2nx+x^2} = \frac{(n-x)(n+x)}{(n+x)^2} = \frac{n-x}{n+x} \)
5. \( \frac{3c-12}{16-c^2} = \frac{3(c-4)}{(4-c)(4+c)} = \frac{-3(4-c)}{(4-c)(4+c)} = \frac{-3}{4+c} \)

Ответ: 1. \( \frac{3a^6}{x^2} \); 2. \( \frac{1}{x+y} \); 3. \( a-y \); 4. \( \frac{n-x}{n+x} \); 5. \( \frac{-3}{4+c} \).