Найдите \(f\left(\frac 53\right)\), если \(f(x) = \frac{x}{x \hspace{0.1cm}-\hspace{0.1cm} 1}\hspace{0.1cm} - \frac 49\).

Решение

Подставим \(x = \frac53: \quad\)

\(f\left(\frac 53\right) = \frac{\frac53}{\frac53 \hspace{0.1cm}-\hspace{0.1cm} 1} \hspace{0.1cm}- \frac 49\ = \frac{\frac53}{\frac23} \hspace{0.1cm}- \frac 49\ = \frac52 \hspace{0.1cm}- \frac 49\ = \frac{37}{18}.\)

Ответ: \(\frac{37}{18}\).