Найдите \(f\left(\dfrac{7}{3}\right)\), если \(f(x) = \dfrac{x}{x - 1} + \dfrac{5}{3}.\)

Решение

Подставим \(x = \dfrac{7}{3}:\)

\[f\left(\dfrac{7}{3}\right) = \dfrac{\dfrac{7}{3}}{\dfrac{7}{3} - 1} + \dfrac{5}{3} = \dfrac{\dfrac{7}{3}}{\dfrac{4}{3}} + \dfrac {5}{3} = \dfrac{7}{4} + \dfrac{5}{3} = \dfrac{41}{12}.\]

Ответ: \(\dfrac{41}{12}\).