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

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

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

Joshua This question is from textbook

Answer by Earlsdon(6294) (Show Source): You can put this solution on YOUR website!
Group the terms in the numerator as follows:
Notice the change of sign in the second group.
Let's do the numerator first:
Factor the first group as the difference of squares and factor a 4 from the second group to get:
Now factor out the common factor of ()
This is the numerator.
Now the denominator:
Factor out a 2.
Putting it all together, we have:
Cancel the indicated factors to leave you with:

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