Algebraic Fraction Help.

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  1. TheMysteryMan's Avatar
    1 07-05-2012  12:25
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    Algebraic Fraction Help.
    Hi, would somebody be able to demonstrate how these type of questions are done. I don't mean to be needy, but could you annotate so I can get a proper understanding.

    Thanks!

    Simplify \frac{6(x+5)^2}{2 (x+5)}

    Simplify \frac{x^2 - 9}{x^2 + 3x}
    Last edited by TheMysteryMan; 07-05-2012 at 12:29.
  2. TenOfThem's Avatar
    2 07-05-2012  12:32
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    Re: Algebraic Fraction Help.
    You look for common factors

    With ordinary numbers you know that

    \dfrac{12}{42} = \dfrac{6\times2}{6\times7} = \dfrac{2}{7}


    You know that you can cancel the 6 x because it is in the numerator and the denominator



    In the same way

    \dfrac{(x+2)(x-5)}{(x+2)(2x+1)}

    has (x+2) multiplying in both the numerator and denominator so it can be cancelled

    \dfrac{(x+2)(x-5)}{(x+2)(2x+1)} = \dfrac{(x+2)\times(x-5)}{(x+2)\times(2x+1)} = \dfrac{x-5}{2x+1}
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  3. Mr M's Avatar
    3 07-05-2012  12:32
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    Re: Algebraic Fraction Help.
    First one, cancel out common factor of x + 5

    Second one factorise the numerator(difference of two squares) and the denominator and then cancel out the common factor of x + 3
  4. TheMysteryMan's Avatar
    4 07-05-2012  13:33
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    Re: Algebraic Fraction Help.
    (Original post by TenOfThem)
    You look for common factors

    With ordinary numbers you know that

    \dfrac{12}{42} = \dfrac{6\times2}{6\times7} = \dfrac{2}{7}


    You know that you can cancel the 6 x because it is in the numerator and the denominator



    In the same way

    \dfrac{(x+2)(x-5)}{(x+2)(2x+1)}

    has (x+2) multiplying in both the numerator and denominator so it can be cancelled

    \dfrac{(x+2)(x-5)}{(x+2)(2x+1)} = \dfrac{(x+2)\times(x-5)}{(x+2)\times(2x+1)} = \dfrac{x-5}{2x+1}
    (Original post by Mr M)
    First one, cancel out common factor of x + 5

    Second one factorise the numerator(difference of two squares) and the denominator and then cancel out the common factor of x + 3
    For the first one, does that become \frac{6(x+5)}{2}
  5. TenOfThem's Avatar
    5 07-05-2012  13:35
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    Re: Algebraic Fraction Help.
    (Original post by TheMysteryMan)
    For the first one, does that become \frac{6(x+5)}{2}
    Apart from the fact that 2 goes into 6, yes
  6. CharlieBoardman's Avatar
    6 07-05-2012  13:36
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    Re: Algebraic Fraction Help.
    (Original post by TheMysteryMan)
    For the first one, does that become \frac{6(x+5)}{2}
    Yes, but it can be made even simpler. Expand the brackets and try to simplify further.
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  7. TheMysteryMan's Avatar
    7 07-05-2012  13:43
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    Re: Algebraic Fraction Help.
    (Original post by CharlieBoardman)
    Yes, but it can be made even simpler. Expand the brackets and try to simplify further.
    \frac{6(x+5)}{2} = \frac{6x+30}{2}
    3x+15 ?
  8. CharlieBoardman's Avatar
    8 07-05-2012  13:45
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    Re: Algebraic Fraction Help.
    (Original post by TheMysteryMan)
    \frac{6(x+5)}{2} = \frac{6x+30}{2}
    3x+15 ?
    Correct
  9. tomctutor's Avatar
    9 07-05-2012  13:45
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    Re: Algebraic Fraction Help.
    Remember to exclude values of x that make the denominator zero - from the domain:
    first one: x =/= -5
    second one: x =/= 0, -3 in your final answer!
  10. Mr M's Avatar
    10 07-05-2012  13:45
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    Re: Algebraic Fraction Help.
    (Original post by TheMysteryMan)
    \frac{6(x+5)}{2} = \frac{6x+30}{2}
    3x+15 ?
    Yes but I would suggest dividing the 6 by 2 would be a better move.
  11. Mr M's Avatar
    11 07-05-2012  13:46
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    Re: Algebraic Fraction Help.
    (Original post by tomctutor)
    Remember to exclude values of x that make the denominator zero - from the domain:
    first one: x =/= -5
    second one: x =/= 0, -3 in your final answer!
    At this level, that is not necessary.
  12. TheMysteryMan's Avatar
    12 07-05-2012  13:47
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    Re: Algebraic Fraction Help.
    (Original post by tomctutor)
    Remember to exclude values of x that make the denominator zero - from the domain:
    first one: x =/= -5
    second one: x =/= 0, -3 in your final answer!
    You lost me
  13. TheMysteryMan's Avatar
    13 07-05-2012  13:50
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    Re: Algebraic Fraction Help.
    For the 2nd one, am I factorising top and bottom first?
  14. TenOfThem's Avatar
    14 07-05-2012  13:50
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    Re: Algebraic Fraction Help.
    (Original post by TheMysteryMan)
    You lost me
    don't worry ... he was answering a more complex question
  15. CharlieBoardman's Avatar
    15 07-05-2012  13:51
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    Re: Algebraic Fraction Help.
    (Original post by TheMysteryMan)
    You lost me
    Don't worry, you do not need to know that yet.
  16. TheMysteryMan's Avatar
    16 07-05-2012  13:57
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    Re: Algebraic Fraction Help.
    (Original post by TenOfThem)
    don't worry ... he was answering a more complex question

    (Original post by CharlieBoardman)
    Don't worry, you do not need to know that yet.
    Ok, would you be able to explain the 2nd one a little more to me, not sure where to start. Am I factorising out the top and bottom?
  17. CharlieBoardman's Avatar
    17 07-05-2012  14:01
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    Re: Algebraic Fraction Help.
    (Original post by TheMysteryMan)
    Ok, would you be able to explain the 2nd one a little more to me, not sure where to start. Am I factorising out the top and bottom?
    Yes, but try to look for the 'difference of two squares' somewhere. Once the numerator and denominator have been factorised correctly, they should have a term in common which you will be able to cancel.
    Last edited by CharlieBoardman; 07-05-2012 at 14:11.
  18. TheMysteryMan's Avatar
    18 07-05-2012  14:03
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    Re: Algebraic Fraction Help.
    I don't think i've been taught that, only the quadratic formula, factorising and graphs.
  19. GreenLantern1's Avatar
    19 07-05-2012  14:09
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    Re: Algebraic Fraction Help.
    (Original post by TheMysteryMan)
    I don't think i've been taught that, only the quadratic formula, factorising and graphs.
    You've not been taught the difference of two squares?

    x^2-4=x^2-2^2=(x+2)(x-2)

    Hence difference of squares?
  20. TheMysteryMan's Avatar
    20 07-05-2012  14:10
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    Re: Algebraic Fraction Help.
    Is the answer -3?
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