Simplify and state the domain:
x'2 +1 . x'2 - 9
x'2 + 2x – 3 x'2 – 2x -3
To simplify the expression and state the domain, we can start by factoring both the numerator and the denominator.
For the numerator x^2 + 2x – 3, we need to find two binomials whose product gives us this expression. The factors are (x + 3) and (x - 1). So, the numerator can be factored as (x + 3)(x - 1).
For the denominator x^2 - 2x - 3, we need to find two binomials whose product gives us this expression. The factors are (x - 3) and (x + 1). So, the denominator can be factored as (x - 3)(x + 1).
Now, we have the simplified expression:
(x + 3)(x - 1)
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(x - 3)(x + 1)
To state the domain, we need to consider the values of x that would make the denominator zero. In this case, both (x - 3) and (x + 1) cannot be zero, so x cannot be equal to 3 or -1.
Therefore, the domain of the simplified expression is all real numbers except for x = 3 and x = -1.