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Math Help - How to multiply algebraic fractions?

  1. #1
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    How to multiply algebraic fractions?

    x+1/3 * 3x+3/2

    As I would do with a normal fraction (I was told to treat algebraic fractions as normal ones) I would multiply the numerator and denominator to get;

    (x+1)(3x+3)/6

    My answer was wrong. Why? And how do you do it? Step by step would be appreciated.
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  2. #2
    MHF Contributor ebaines's Avatar
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    Re: How to multiply algebraic fractions?

    To be clear, your oiginal equation i:

     \frac {x+1} 3 \times \frac {3x+3} 2

    right? If so, your answer is correct:

     \frac {x+1} 3 \times \frac {3x+3} 2 = \frac {(x+1)(3x+3)} 6

    but note that it can be simplified:   \frac {(x+1)(3x+3)} 6 = \frac {(x+1)3(x+1)} 6= \frac {(x+1)^2} 2

    What answer did they give you?
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  3. #3
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    Re: How to multiply algebraic fractions?

    The one you arrived on, the simplification.
    Hmm, where did the 3 go and why did the denominator turn into 2?
    Thanks a lot!
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  4. #4
    MHF Contributor ebaines's Avatar
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    Re: How to multiply algebraic fractions?

    Quote Originally Posted by Ashir View Post
    Hmm, where did the 3 go and why did the denominator turn into 2?
    Thanks a lot!
    Simplifying fractions - the 3's in the numerator and denominator cancel out:

     \frac {(x+1)(3x+3)} 6 = \frac {(x+1)3(x+1)} 6= \frac {3(x+1)^2} { 3 \times 2} = \frac {(x+1)^2} 2
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  5. #5
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    Re: How to multiply algebraic fractions?

    Ah, right. Thanks!
    Is there a way for me to tell if I should have factorize the bracket, because I didn't know I should have factorized 3x+3.
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  6. #6
    MHF Contributor ebaines's Avatar
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    Re: How to multiply algebraic fractions?

    In general you want to get rid of common factors that are in both numerator and denominator. As for factoring - it's best to group like terms when you can. Hence 3(x+1) is a better representation than 3x+3.
    Last edited by ebaines; October 22nd 2012 at 10:45 AM.
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  7. #7
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    Re: How to multiply algebraic fractions?

    What do you mean by 'group like terms'? How did you do this here?
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  8. #8
    MHF Contributor ebaines's Avatar
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    Re: How to multiply algebraic fractions?

    The expression 3x+3 has the number '3' in it twice. So we say that 3 and 3x have "like terms," and we can pull the 3 out so it appears only once: 3x+3 = 3(x+1).
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  9. #9
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    Re: How to multiply algebraic fractions?

    I know what like terms are but how is that grouping if you extracted the 3? Isn't that the opposite?
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  10. #10
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    Re: How to multiply algebraic fractions?

    Actually I got it now, you're grouping the x+1's. Thanks for the help!
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