2. Выполните действия: a) \(\frac{a+b}{a-b} + \frac{a}{b}\) б) \(\frac{3x^2}{x^2-1} - \frac{3x}{x-1}\) в) \(\frac{2y^2}{y-8} - 2y\)

2. Выполните действия:

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

Ответ: а) \(\frac{a^2+b^2}{ab-b^2}\); б) \(\frac{-3x}{x^2-1}\); в) \(\frac{16y}{y-8}\).