4) \(\frac{c-1}{c-2}-\frac{2}{c+1}=\)

Общий знаменатель: \((c-2)(c+1)\).

\[\frac{c-1}{c-2}-\frac{2}{c+1}=\frac{(c-1)(c+1)-2(c-2)}{(c-2)(c+1)}=\frac{c^2-1-2c+4}{(c-2)(c+1)}=\frac{c^2-2c+3}{(c-2)(c+1)}.\]

ОДЗ: \(c\ne 2\), \(c\ne -1\).

Ответ: \(\frac{c^2-2c+3}{(c-2)(c+1)}\).