The critical values are

`x = −3`, `x = 2` and `x = 4`.

These critical values divide the number line into 4 intervals.

Hence, the signs of the function are:

Interval `((x−2)^2(x+3))/(4−x)` sign of f(x)
`x < −3` Signs of numerator and denominator
`−3 < x < 2` Signs of numerator and denominator +
`2 < x < 4` Signs of numerator and denominator +
`x > 4` Signs of numerator and denominator

Since we want `f(x) < 0`, the intervals that satisfy this inequality will be those with a negative sign.

Hence, the solution is: `x < −3` or `x > 4`.

Here's the graph of the solution.

123450-1-2-3-4xOpen image in a new page

Please support IntMath!