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Help me understand this Solution:

  1. Mar 25, 2008 #1
    It is a case of simplifying this expression:

    a^2 - ab / ab



    The solution given in a textbook is:

    a - b / b



    I observe that for the one "a" that was canceled below, two "a's" were canceled above in this simplification.


    Why would the solution not be: a^2 - b / b? I would like to know what happened to the a in a^2 if the textbook answer is the correct answer.


    I am also having problems simplifying this expression: 3y^2 - 27 / 12y^2 + 36y
    I have tried factorizing to find common factors that cancel each other out but have not had any success.... I know what the solution is but I would like to know how to get there.
     
    Last edited: Mar 25, 2008
  2. jcsd
  3. Mar 25, 2008 #2

    HallsofIvy

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    No, only one a was canceled in both numerator and denominator. Remember that you can only cancel things that are multiplied. You are thinking
    "Okay, I will cancel the last a in a2- ab with the a in the denominator and get (a2-b)/b."

    but you can't do that: the second a is not a factor. What you need to do is first factor a2- ab= a(a- b). NOW you can cancel:
    [tex]\frac{a^2- ab}{ab}= \frac{a(a-b)}{ab}= \frac{a- b}{b}[/tex]
    where you have canceled the a multiplying (a- b) in the numerator with the a multiplying b in the denominator.
     
  4. Mar 25, 2008 #3

    tiny-tim

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    Welcome to PF!

    Hi Bardagath! Welcome to PF! :smile:

    I suspect you're having vision problems … you can't take in the whole top line in one go.

    Just split it into two fractions, then factor it …

    (a^2)/b - ab/b = … ? :smile:
    With ordinary fractions (just numbers), if asked to simplify 21/4, you might say [tex]5\frac{1}{4}\,.[/tex]

    5 is the "whole" multiple, and 1 is the remainder.

    With polynomial fractions, you do the same … for example, (3x + 11)/(x + 2) = 3 + 5/(x + 2).

    3 is the "whole" multiple, and 5 is the remainder.

    The remainder can be a number, as 5 above, or it can be a polynomial (of lesser degree than the denominator. of course!) :smile:
     
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