Thank you, but that is not exactly the way for me to figure it out.
Say I don't have the answer in the first place, and simply need to answer the original question, how would i find
r - 3
r + 2
I only said i had the answer in the first place because I am doing a practice test which includes the answers, which usually lets me figure out things backwards, but in this case I do not know how, and certainly will not have the answer to do so on the real test.
I think I see your problem:
We are not using the values r=2 or r=-2.
In fact they are not in the domain of the function so we are not allowed to use them.
lets look at the numerator for a second...
We need to factor this expression loosely speaking un Distribute or FOIL it
To do this we need to compare it to the general form
we can identify a=1 b=-5 and c=6.
Since a=1 when just need to find factors of c (6) that add up to b (-5)
We start by looking at all of the factors of 6 they are
We know that since c is postitive and b is negative that both of our factors need to be negative.
So it seems that these work so we can factor
We can check that the factorization is correct by multiplying it out and seeing if it equals what we started with so lets check
when we collect the like terms we end up with so our factorization checks.
Note: that the denominator can be factored this way, but it is in a special form called the difference of squares that can always be factored using this formula
Hint: for yours remember that