SOLUTION: Solve {{{(3x^2+13x+4)/(x+6)>0}}}

Question 135458: Solve
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Let's graph

So we can see that everything to the right of is in the solution set. So part of our solution is

Start with the given inequality

Set the numerator equal to zero

Factor the left side (note: if you need help with factoring, check out this solver)

Now set each factor equal to zero:
or

or Now solve for x in each case

So the critical values are

or

Now plot the critical values on a number line

So let's evaluate a point that is to the left of

(which is the left most endpoint). Let's evaluate the value

Start with the given inequality

Plug in

Evaluate and simplify

Since

is true, this means that one part of the solution in interval notation is

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Now let's test a point that is in between the critical values

and

Start with the given inequality

Plug in

Evaluate and simplify

Since

is false, this means that the interval does not work. So that means that this interval is not in the solution set and can be ignored.
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So let's evaluate a point that is to the right of

(which is the right most endpoint). Let's evaluate the value

Start with the given inequality