1. Сократите дробь: a) \(\frac{16a^5b}{12a^8b^2}\) б) \(\frac{ab+a^2}{a^2}\) в) \(\frac{x-3y}{x^2-9y^2}\)

1. Сократите дробь:

1. a) \(\begin{aligned}\)\(\frac{16a^5b}{12a^8b^2}\) &= \(\frac{4 · 4 · a^5 · b}{3 · 4 · a^5 · a^3 · b · b}\) \\ &= \(\frac{4}{3a^3b}\) \(\end{aligned}\)
2. б) \(\begin{aligned}\)\(\frac{ab+a^2}{a^2}\) &= \(\frac{a(b+a)}{a^2}\) \\ &= \(\frac{b+a}{a}\) \(\end{aligned}\)
3. в) \(\begin{aligned}\)\(\frac{x-3y}{x^2-9y^2}\) &= \(\frac{x-3y}{(x-3y)(x+3y)}\) \\ &= \(\frac{1}{x+3y}\) \(\end{aligned}\)

Ответ: а) \(\frac{4}{3a^3b}\); б) \(\frac{b+a}{a}\); в) \(\frac{1}{x+3y}\).