1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Simplify the following

  1. Apr 27, 2010 #1
    1. The problem statement, all variables and given/known data
    simplify the following equation

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


    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
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook