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Math Help - Algebraic Fractions?

  1. #1
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    australia
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    Algebraic Fractions?

    Hi,

    I have an equation i cannot work out. The question is simplify the following :Algebraic Fractions?-untitled.jpg

    (equation in image)

    Thanks.
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  2. #2
    Super Member

    Joined
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    Lexington, MA (USA)
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    Re: Algebraic Fractions?

    Hello, jeremyjezzanba!

    First of all, it is not an equation . . . It's an expression.

    Second, exactly where is your difficulty?
    . . You don't understand division?
    . . You don't know how to factor?
    . . You don't know how to reduce?


    \text{Simplify: }\:\frac{x^2-4}{x^2-9} \div \frac{4x+8}{12x-36}

    \frac{x^2-4}{x^2-9} \div \frac{4x+8}{12x-36} \;=\;\frac{x^2-4}{x^2-9} \cdot \frac{12x-36}{4x+8}

    . . . . . . . . . . . . . =\;\frac{(x-2)(x+2)}{(x-3)(x+3)}\cdot\frac{12(x-3)}{4(x+2)}

    . . . . . . . . . . . . . =\;\frac{(x-2)({\color{red}\rlap{/////}}{x+2})}{({\color{blue}\rlap{/////}}x-3)(x+3)}\cdot\frac{{\color{green}\rlap{//}}12^3({\color{blue}\rlap{/////}}x-3)}{{\color{green}\rlap{/}}4({\color{red}\rlap{/////}}x+2)}

    . . . . . . . . . . . . . =\;\frac{3(x-2)}{x+3}
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