SOLUTION: I have a problem where I am supposed to write each rational expression in lowest terms after factoring. The problem is: m^2 - n^2 - 4m - 4n -------------------- 2m - 2n - 8

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Question 194088This question is from textbook
: I have a problem where I am supposed to write each rational expression in lowest terms after factoring. The problem is:
m^2 - n^2 - 4m - 4n
--------------------
2m - 2n - 8
The back of the book gives an answer of m +n but I can't figure out how to get it ------
2
I can get as far as
(m - n)(m + n)-4(m + n)
-----------------------
2(m - n - 4)
and I do not know how to simplify further
Thanks in advance for the help and I apologize if I submitted this in the wrong place

JoshuaThis question is from textbook

Answer by Earlsdon(6103) About Me  (Show Source):
You can put this solution on YOUR website!
%28m%5E2-n%5E2-4m-4n%29%2F%282m-2n-8%29 Group the terms in the numerator as follows:
%28%28m%5E2-n%5E2%29-highlight_green%28%284m%2B4n%29%29%29%2F%282m-2n-8%29 Notice the change of sign in the second group.
Let's do the numerator first:
%28m%5E2-n%5E2%29-%284m%2B4n%29 Factor the first group as the difference of squares and factor a 4 from the second group to get:
%28m-n%29%2Ahighlight%28%28m%2Bn%29%29-4%2Ahighlight%28%28m%2Bn%29%29 Now factor out the common factor of (highlight%28m%2Bn%29)
%28m%2Bn%29%28m-n-4%29 This is the numerator.
Now the denominator:
2m-2n-8 Factor out a 2.
2%28m-n-4%29 Putting it all together, we have:
%28m%2Bn%29highlight_green%28%28m-n-4%29%29%2F%282%2Ahighlight_green%28%28m-n-4%29%29%29 Cancel the indicated factors to leave you with:
highlight%28%28m%2Bn%29%2F2%29