2. Solve for x
Find the roots of the top
and the roots of the bottom
Divide the number line up into the intervals between these roots, and pick a point in each interval.
In the first interval the simplest point is -4.
Two negatives give us a positive answer, so -4 is a solution and so are all the points in the first interval.
In the next interval the simplest point is 0.
A negative over a positive is negative, so 0 is not a solution and neither are any of the other points in the second interval.
In the last interval, the simplest point is 2
f(2) = ((2 - 1)/((2 + 3)
= 1/5 > 0
A positive over a positive is positive, so 2 is a solution and so is every point in the last interval. We darken in all the points in the first and last interval. The last question is what about the endpoints. At the root of the top, 1, we get a 0 on top, so the whole fraction is 0 which is all right in this inequality, so 1 is a solution. We darken in the point at 1. At the root of the bottom, -3, the bottom is 0, and so the fraction does not have a real number solution, so we can't tell if the answer is positive or negative. -3 is not a solution. Leave the point at -3 open.