m 3 m2 9 3 m m 3 1 2 m 5m 6 m 2 1

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Unformatted text preview: lems] (b) m2 - 9 3-m ¸ 2 m + 5m + 6 m + 2 With division problems it is very easy to mistakenly cancel something that shouldn’t be canceled and so the first thing we do here (before factoring!!!!) is do the division. Once we’ve done the division we have a multiplication problem and we factor as much as possible, cancel everything that can be canceled and finally do the multiplication. So, let’s get started on this problem. m2 - 9 3-m m2 - 9 m+2 ¸ =2 × 2 m + 5m + 6 m + 2 m + 5m + 6 3 - m ( m - 3)( m + 3) × ( m + 2 ) = ( m + 3)( m + 2 ) ( 3 - m ) Now, notice that there will be a lot of canceling here. Also notice that if we factor a minus sign out of the denominator of the second rational expression. Let’s do some of the canceling and then do the multiplication. ( m - 3) m2 - 9 3 - m ( m - 3) 1 ¸ = × = 2 m + 5m + 6 m + 2 1 - ( m - 3) - ( m - 3) Remember that when we cancel all the terms out of a numerator or denominator there is actually © 2007 Paul Dawkins 46 http://tutorial.math.lamar.edu/terms.aspx College Algebra a “1” left over! Now, we didn’t finish the cancelin...
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