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

Algebra.Com's Answer #145682 by Earlsdon(6294) $\"\"$ $\"About$

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:
\n" ); document.write( " $\"%28%28m%5E2-n%5E2%29-highlight_green%28%284m%2B4n%29%29%29%2F%282m-2n-8%29\"$ Notice the change of sign in the second group.
\n" ); document.write( "Let's do the numerator first:
\n" ); document.write( " $\"%28m%5E2-n%5E2%29-%284m%2B4n%29\"$ Factor the first group as the difference of squares and factor a 4 from the second group to get:
\n" ); document.write( " $\"%28m-n%29%2Ahighlight%28%28m%2Bn%29%29-4%2Ahighlight%28%28m%2Bn%29%29\"$ Now factor out the common factor of ( $\"highlight%28m%2Bn%29\"$ )
\n" ); document.write( " $\"%28m%2Bn%29%28m-n-4%29\"$ This is the numerator.
\n" ); document.write( "Now the denominator:
\n" ); document.write( " $\"2m-2n-8\"$ Factor out a 2.
\n" ); document.write( " $\"2%28m-n-4%29\"$ Putting it all together, we have:
\n" ); document.write( " $\"%28m%2Bn%29highlight_green%28%28m-n-4%29%29%2F%282%2Ahighlight_green%28%28m-n-4%29%29%29\"$ Cancel the indicated factors to leave you with:
\n" ); document.write( " $\"highlight%28%28m%2Bn%29%2F2%29\"$ \n" ); document.write( "

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