(2x+y)(2x-y) what is this equation
2 answers:
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Answer:
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, ∞)
