119. (\(\frac{4x}{x + 2} + 2x\)) \cdot \(\frac{x + 2}{4x^2}\).

119. Упростим выражение:

\((\frac{4x}{x + 2} + 2x\)) \cdot \(\frac{x + 2}{4x^2}\) = \((\frac{4x + 2x(x + 2)}{x + 2}\)) \cdot \(\frac{x + 2}{4x^2}\) = \((\frac{4x + 2x^2 + 4x}{x + 2}\)) \cdot \(\frac{x + 2}{4x^2}\) = \((\frac{2x^2 + 8x}{x + 2}\)) \cdot \(\frac{x + 2}{4x^2}\) = \(\frac{2x(x + 4)}{x + 2}\) \cdot \(\frac{x + 2}{4x^2}\) = \(\frac{2x(x + 4)(x + 2)}{(x + 2)4x^2}\) = \(\frac{2x(x + 4)}{4x^2}\) = \(\frac{x + 4}{2x}\)

Ответ: \(\frac{x + 4}{2x}\)