Question

Solve:

$\frac{(x-4{)}^{1999}(2x+4{)}^{2006}(8x+9{)}^{2007}}{(x-8{)}^{2004}(x+9{)}^{2005}}\ge 0$

Answer 1

factors with odd power can have sign change but factors\\with even power can be either 0 or +ve.

$\therefore x\in (-9,-2]\cup \left[\right(\frac{-9}{8}),4]\cup (8,\infty )$