You have four critical points where things could change: .
Plot those four points on a number line and make a sign diagram by plugging in a number from each of the 5 regions you've created to see if you get a positive or a negative.
Hello, great_math!
Edit: Henderson has already supplied the analysis . . .
Find the solution: .
Consider graphing the function.
There are x-intercepts at: . (multiplicity 2)
There is a vertical asymptote: .
. . Note: there is a horizontal asymptote,
Testing values in each interval, we find:
. .
The graph looks like this:Code:: | :* | * : | * * : * |* * : * * | * * * - - - - - - : - - o - + - -o- - - - -o- - - - - - - - - * : -2/5 | 1/3* * 2 * : | * * : | *: | -2 |
Solution: .