Answer:
The correct option is 2.
Step-by-step explanation:
The given rational expression is
Factorize the denominator.
The middle term can be written as 5x+x.
Cancel out the common factors.
The simplified form of the given expression is . The factors of the denominator are (x+5) and (x+1), it means at x=-5 and x=-1, the value of denominator is zero.
The given expression is not defined for x=-1 and x=-5.
Therefore the correct option is 2.
First of all, we can observe that
So the expression becomes
This means that the expression is defined for every
Now, since the denominator is always positive (when it exists), the fraction can only be positive if the denominator is also positive: we must ask
Since we can't accept 3 as an answer, the actual solution set is