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Simplifying a fraction

  1. Dec 28, 2015 #1
    1. The problem statement, all variables and given/known data
    Simplify (6x+12y)/(10a +5) times (100a2 - 25)/(9x2 - 81y2)

    2. Relevant equations
    (6x+12y)/(10a +5) times (100a2 - 25)/(9x2 - 81y2)

    3. The attempt at a solution
    (6x+12y)/(10a +5) times (100a2 - 25)/(9x2 - 81y2) =
    3(2x+4y)/(10a+5) times (4a - 1)/(3x-27y) = (3(2x+4y))(4a-1)/(5(2a+1))(3(x-9y))
    I do not know how to simplify this any further.
     
    Last edited: Dec 28, 2015
  2. jcsd
  3. Dec 28, 2015 #2

    SammyS

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    If you learn a little bit of LaTeX, you can make this look nicer.

    How did ##\displaystyle \ \frac{(100a^2-25)}{(9x^2-81y^2)} \ ## become ##\displaystyle \ \frac{(10a-5)}{(3x-9y)} \ ## ?
     
  4. Dec 28, 2015 #3
    Let me try this again and see what I come up with
     
  5. Dec 28, 2015 #4
    (6x+12y)/(10a+5) times (100a2 - 25)/(9x2 - 81y2) = (3(x+4y))/(5(2a+1)) times (5(20a2 - 5))/(3(3x2 - 27y2))
     
  6. Dec 28, 2015 #5

    SammyS

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    Let's look at the individual factors, (individual numerators & denominators).

    The first fraction is fine, both numerator & denominator are totally factored.

    You can factor out an additional 5 from 100a2 - 25 = 5(20a2 - 5), which will get you back to a difference of squares for one of the factors, and thus can be factored even further.

    Similarly, you can factor out an additional 3 from 9x2 - 81y2 = 3(3x2 - 27y2), which will get you back to a difference of squares for one of the factors, and thus can be factored even further.

    Then put all into one grand rational expression ("fraction") & do some further cancelling.
     
  7. Dec 28, 2015 #6
    I think i made a mistake: (3(x+4y))/(5(2a+1)) times (5(20a2 - 5))/(3(3x2 - 27y2))
    (3(x+4y)) should have been: (3(2x+4y))
     
  8. Dec 28, 2015 #7

    SammyS

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    Right.

    You had that part correct previously.
     
  9. Dec 28, 2015 #8
    The only factoring I can see to do is: (5(20a2 + 5))/(3(3x2 - 27y2)) = (4a2 +1)/(x2 - 9y2) and then put these together: (3(2x + 4y))(4a2 + 1)/(5(2a +1))(x2-9y2)
     
  10. Dec 28, 2015 #9

    SammyS

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    You can't just drop factors for no reason.

    Start with 5(20a2 - 5) = 5⋅5(4a2 -1) . (Yes, that is subtraction.)

    Do you know how to factor a difference of squares?

    Similarly, 3(3x2 - 27y2) = 3⋅3(x2 - 9y2) . Also has a difference of squares.
     
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