Solving rational inequalities and use sign diagram to sketch the graph. image attached for better understanding.

x ∈ (-2, -1) ∪ (1/3, ∞)

Step-by-step explanation:

To solve this problem we must factor the expression that is shown in the Numerator of the inequality.

So, we have:

We should look for two numbers that add 2/3 as a result and multiply as a result -1/3

These numbers are -1/3 and 1

Then:

So the roots are:

Now the expression is as follows:

Now we use the study of signs to solve this inequality.

We have 3 roots for the polynomials that compose the expression:

We know that x = -2 is not in the domain of the function because it makes the denominator equal to zero

With these roots we make the study of signs:

Observe the attached image.

Note that:

when

when

when

Finally after the study of signs we can reach the conclusion that:

x ∈ (-2, -1) ∪ (1/3, ∞)

the surface area is 124cm²

step-by-step explanation:

length: 4cm

width: 9cm

height:   2cm