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

x ∈ (-∞, -1) ∪ (1, ∞)

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 make up the expression:

We know that the first two are not allowed because they make the denominator zero.

Observe the attached image.

Note that:

when

when

and

is always

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

x ∈ (-∞, -1) ∪ (1, 2] ∪ [2, ∞)

This is the same as

x ∈ (-∞, -1) ∪ (1, ∞)

b

step-by-step explanation: