Results 1 to 7 of 7

Math Help - Having sign problem with algebraic fractions

  1. #1
    Junior Member
    Joined
    Jan 2013
    From
    Montreal
    Posts
    65
    Thanks
    1

    Having sign problem with algebraic fractions

    Hi,

    I'm having a problem with an algebraic fractions equation. It goes:

    5/3(v-1) + (3v-1)/(1-v)(1+v) + 1/2(v+1)

    The first thing I do is factor out the negative in the first fraction, getting:

    -5/3(1-v)

    Giving a cd of 6(1-v)(v+1). Now that that is done I multiply the numerators by the necessary factors:

    -5*2(v+1)

    6(3v-1)

    3(1-v)

    Which gives me -10v -10 + 18v -6 -3v + 3

    Which adds up to 5v - 13

    BUT the answer is -5v + 13, and if I factor out the negative in the second equation, all the signs are reversed and the equation works out to the right answer. So I'm confused as to why things didn't work when I factored out the negative in the first fraction.

    Thanks,

    Kevin
    Last edited by KevinShaughnessy; January 26th 2013 at 06:04 PM.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Joined
    Sep 2012
    From
    Australia
    Posts
    3,695
    Thanks
    619

    Re: Having sign problem with algebraic fractions

    Hey KevinShaughnessy.

    Can you clarify whether (3v-1)/(1-v)(1+v) is (3v-1)(1+v) / (1-v) or (3v-1) / [(1+v)(1-v)]?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Super Member

    Joined
    May 2006
    From
    Lexington, MA (USA)
    Posts
    11,749
    Thanks
    650

    Re: Having sign problem with algebraic fractions

    Hello, Kevin!

    There is nothing wrong with your work or your answer.
    They approached the problem differently . . . that's all.
    Both answers are correct.


    \text{Simplify: }\:\frac{5}{3(v-1)} + \frac{3v-1}{(1-v)(1+v)} + \frac{1}{2(v+1)}

    They factored a "minus" out of the second fraction.

    . . \frac{5}{3(v-1)} - \frac{3v-1}{(v-1)(v+1)} + \frac{1}{2(v+1)}


    The LCD is 6(v-1)(v+1)\!:

    . . \frac{5}{3(v-1)}\cdot {\color{blue}\frac{2(v+1)}{2(v+1)}} - \frac{3v-1}{(v-1)(v+1)}\cdot {\color{blue}\frac{6}{6}} + \frac{1}{2(v+1)}\cdot {\color{blue}\frac{3(v-1)}{3(v-1)}}

    . . =\;\frac{10(v+1)}{6(v-1)(v+1)} - \frac{6(3v-1)}{6(v-1)(v+1)} + \frac{3(v-1)}{6(v-1)(v+1)}

    . . =\;\frac{10v + 10 - 18v + 6 + 3v - 3}{6(v-1)(v+1)}

    . . =\;\frac{13-5v}{6(v-1)(v+1)}
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Junior Member
    Joined
    Jan 2013
    From
    Montreal
    Posts
    65
    Thanks
    1

    Re: Having sign problem with algebraic fractions

    Quote Originally Posted by chiro View Post
    Hey KevinShaughnessy.

    Can you clarify whether (3v-1)/(1-v)(1+v) is (3v-1)(1+v) / (1-v) or (3v-1) / [(1+v)(1-v)]?
    It's (3v-1) / [(1+v)(1-v)].
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Junior Member
    Joined
    Jan 2013
    From
    Montreal
    Posts
    65
    Thanks
    1

    Re: Having sign problem with algebraic fractions

    Quote Originally Posted by Soroban View Post
    Hello, Kevin!

    There is nothing wrong with your work or your answer.
    They approached the problem differently . . . that's all.
    Both answers are correct.



    They factored a "minus" out of the second fraction.

    . . \frac{5}{3(v-1)} - \frac{3v-1}{(v-1)(v+1)} + \frac{1}{2(v+1)}


    The LCD is 6(v-1)(v+1)\!:

    . . \frac{5}{3(v-1)}\cdot {\color{blue}\frac{2(v+1)}{2(v+1)}} - \frac{3v-1}{(v-1)(v+1)}\cdot {\color{blue}\frac{6}{6}} + \frac{1}{2(v+1)}\cdot {\color{blue}\frac{3(v-1)}{3(v-1)}}

    . . =\;\frac{10(v+1)}{6(v-1)(v+1)} - \frac{6(3v-1)}{6(v-1)(v+1)} + \frac{3(v-1)}{6(v-1)(v+1)}

    . . =\;\frac{10v + 10 - 18v + 6 + 3v - 3}{6(v-1)(v+1)}

    . . =\;\frac{13-5v}{6(v-1)(v+1)}
    But aren't the two answers fundamentally different being that one produces a negative number and the other produces the same number but positive?
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Member
    Joined
    Feb 2010
    From
    in the 4th dimension....
    Posts
    122
    Thanks
    9

    Re: Having sign problem with algebraic fractions

    Quote Originally Posted by KevinShaughnessy View Post
    But aren't the two answers fundamentally different being that one produces a negative number and the other produces the same number but positive?
    perhaps you misread the answer and you should check it again...
    your answer was  \frac{5v-13}{6{\color{magenta}(1-v)}(1+v)} while most probably the answer in your book is given as \frac{13-5v}{6{\color{magenta}(v-1)}(1+v)}, Which you know are the same answers because the answer in your book changed your (1-v) to (v-1) by multiplying the numerator and denominator by -1.
    Follow Math Help Forum on Facebook and Google+

  7. #7
    Junior Member
    Joined
    Jan 2013
    From
    Montreal
    Posts
    65
    Thanks
    1

    Re: Having sign problem with algebraic fractions

    Quote Originally Posted by earthboy View Post
    perhaps you misread the answer and you should check it again...
    your answer was  \frac{5v-13}{6{\color{magenta}(1-v)}(1+v)} while most probably the answer in your book is given as \frac{13-5v}{6{\color{magenta}(v-1)}(1+v)}, Which you know are the same answers because the answer in your book changed your (1-v) to (v-1) by multiplying the numerator and denominator by -1.
    It has all become clear hah. Thank you everyone!
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Algebraic Fractions
    Posted in the Algebra Forum
    Replies: 2
    Last Post: June 17th 2011, 01:27 AM
  2. [SOLVED] Algebraic Fractions
    Posted in the Algebra Forum
    Replies: 3
    Last Post: May 9th 2011, 03:39 AM
  3. Replies: 0
    Last Post: April 28th 2010, 09:53 AM
  4. algebraic fractions
    Posted in the Algebra Forum
    Replies: 1
    Last Post: June 1st 2009, 06:11 PM
  5. Sign problem on complex fractions
    Posted in the Algebra Forum
    Replies: 7
    Last Post: May 7th 2009, 08:24 PM

Search Tags


/mathhelpforum @mathhelpforum