Найдите \(f\left(\frac 35\right)\), если \(f(x) = \frac{x}{1 \hspace{0.1cm}- \hspace{0.1cm}x}\hspace{0.1cm} - \frac 57\).

Решение

Подставим \(x = \frac35:\) \(f\left(\frac 35\right) = \frac{\frac35}{1 \hspace{0.1cm}-\hspace{0.1cm} \frac35}\hspace{0.1cm} - \frac 57\ = \frac{\frac35}{\frac25} \hspace{0.1cm}- \frac 57\ = \frac32 \hspace{0.1cm}- \frac 57\ = \frac{11}{14}.\)

Ответ: \(\frac{11}{14}\).