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

x ∈ (-∞, -2) ∪ (2, ∞)

Step-by-step explanation:

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

So, we have:

So the roots are:

Therefore we can write the expression in the following way:

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:

.

Observe the attached image.

We know that the first two roots are not allowed because they make zero the denominator, we also know that (x + 5) ^ 2 is always positive because it is squared, so it is not necessary to include the numerator in the study of signs.  

Note that:

when

when

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

x ∈ (-∞, -2) ∪ (2, ∞)

45

step-by-step explanation: