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Homework Help: Simplify the following

  1. Apr 27, 2010 #1
    1. The problem statement, all variables and given/known data
    simplify the following equation
    ((20*(4*x-1)^4)/(3*x+5)^7)-((4*x-1)^5/(21*(3*x+5)^8))

    3. The attempt at a solution
    i took (4*x-1)^4)/(3*x+5)^7) as a common factor and ended up with

    (4*x-1)^4)/(3*x+5)^7)*(20-((4*x-1)^5/(21*(3*x+5)^8)))

    can someone show me how to simplify this all the way, step by step please so i know how to do it for other questions =)
     
  2. jcsd
  3. Apr 27, 2010 #2
    I would multiply by [tex] 21(3x+5)^8 [/tex] so

    [tex] = 20(4x-1)^4\times21(3x+5) - (4x-1)^5 [/tex]

    Then Factor out [tex] (4x-1)^4 [/tex]

    [tex] = (4x-1)^4\times[420(3x+50)-(4x-1)] [/tex]

    Simplify Inside Brackets.
     
  4. Apr 29, 2010 #3
    that comes out with (4x-1)^4 (1256 x+2101) which is wrong, anybody else no how to simplify this problem?
     
  5. Apr 29, 2010 #4
    OOOPS! My bad. You are right. I actually just multiplied the whole thing by 21(3x+5)^8 which does not equal 1 so I changed the function. Here is another try which is right (I graphed them both and they are the same) I just do not know if it is completely simplified:

    [tex] \frac{20(4x-1)^4}{(3x+5)^7} - \frac{(4x-1)^5}{21(3x+5)^8}

    = \frac{(4x-1)^4}{(3x+5)^7}\left[20 - \frac{4x-1}{21(3x+5)}\right]

    = \frac{(4x-1)^4}{(3x+5)^7}\left[\frac{20*21(3x+5)-(4x-1)}{21(3x+5)}\right]

    = \frac{(4x-1)^4}{21(3x+5)^8}(1256x+2101) [/tex]

    Notice it is the same answer as before just divided by 21(3x+5)^8, so that WOULD be multiplying the function by 1 and thus not change it. Also, 1256 and 2101 do not have any common factors but 1 so that cannot be simplified more.
     
    Last edited: Apr 29, 2010
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