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Math Help - How to reduce this function completely

  1. #1
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    How to reduce this function completely



    The question is asking, "In the reduced form the numerator is:".

    Please explain to me in steps how I can do this.

    Thank You
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  2. #2
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    Re: How to reduce this function completely

    Quote Originally Posted by ritacame View Post

    The question is asking, "In the reduced form the numerator is:".
    Please explain to me in steps how I can do this.
    In factored form it is: \frac{x}{(x+3)(x+5)}-\frac{x}{(x+3)(x-3)}-\frac{5}{(x-3)(x+5)}.

    So what is the LCD?
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  3. #3
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    Re: How to reduce this function completely

    Is it 3?
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  4. #4
    MHF Contributor Siron's Avatar
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    Re: How to reduce this function completely

    If you look at the denominators of the separated fractions they almost have some factor(s) in common.
    We have:
    \frac{x}{(x+3)(x+5)}-\frac{x}{(x+3)(x-3)}-\frac{5}{(x-3)(x+5)}

    Multipliy the first term with \frac{x-3}{x-3}
    Multiply the second term with \frac{x+5}{x+5}
    Multiply the third term with \frac{x+3}{x+3}

    And so we get:
    \frac{x(x-3)}{(x+3)(x+5)(x-3)}-\frac{x(x+5)}{(x+3)(x-3)(x+5)}-\frac{5(x+3)}{(x-3)(x+5)(x+3)}=\frac{x(x-3)-x(x+5)-5(x+3)}{(x+3)(x-3)(x+5)}

    Now they've all the same denominator.
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