## Precalculus (6th Edition) Blitzer

Domain: $(-\infty,-5)\cup(2,\infty)$
Logarithmic functions are defined for positive arguments only. $f(x)=\displaystyle \ln(\frac{x-2}{x+5})$ is defined for $\displaystyle \frac{x-2}{x+5}\gt 0.$ The boundary points are $-5$ and $2.$ Testing each interval $:$ $\left[\begin{array}{llllllll} & -\infty & & -5 & & 2 & & \infty\\ \text{test point} & & -10 & & 0 & & 10 & \\ f(x) & & \frac{-12}{-15} & & \frac{-2}{5} & & \frac{8}{15} & \\ \text{sign} & & + & & - & & + & \end{array}\right]$ Domain: $(-\infty,-5)\cup(2,\infty)$ .