1. Сократите дробь: a) \(\frac{14a^3b^5}{21a^4b^3}\) б) \(\frac{x^2+x}{x^2}\) в) \(\frac{a+2b}{a^2-4b^2}\)

1. Сокращение дробей:

1. а) \(\begin{aligned}\)\(\frac{14a^3b^5}{21a^4b^3}\) &= \(\frac{2 \cdot 7 \cdot a^3 \cdot b^3 \cdot b^2}{3 \cdot 7 \cdot a^3 \cdot a \cdot b^3}\) \\ &= \(\frac{2b^2}{3a}\)\(\end{aligned}\)


2. б) \(\begin{aligned}\)\(\frac{x^2+x}{x^2}\) &= \(\frac{x(x+1)}{x^2}\) \\ &= \(\frac{x+1}{x}\)\(\end{aligned}\)


3. в) \(\begin{aligned}\)\(\frac{a+2b}{a^2-4b^2}\) &= \(\frac{a+2b}{(a-2b)(a+2b)}\) \\ &= \(\frac{1}{a-2b}\)\(\end{aligned}\)

Ответ: а) \(\frac{2b^2}{3a}\); б) \(\frac{x+1}{x}\); в) \(\frac{1}{a-2b}\).