$\begin{array}{ll}\text { Since } & f^{\prime}(x)=\frac{3}{(x+1)^2} \text { is greater than '0' in interval }(-\infty, \infty) \text {, therefore } f(x)=\frac{x-2}{x+1} \text { is increasing in interval } \\ \text { is }\end{array}$ $(-\infty, \infty)$ or $R$.