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Math Help - Confused on how a complex polynomial fractions are simplified in sample problems

  1. #1
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    Confused on how a complex polynomial fractions are simplified in sample problems

    I am taking an intermediate algebra course and am stumped on one topic. We are doing complex polynomial fractions and I can figure out how they are simplifying one type of problem. Here is an example:

    7 14
    ___ - ____ 7x2 -14x 7x
    x x2 ___________________ ____________
    _________________________ I keep coming up with but am told the answer is simplified to
    4 16 4x2 -16 4(x+2)
    ____ - ____
    x x3


    Please help me understand how this is being simplified. THANKS!!!!
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    Re: Confused on how a complex polynomial fractions are simplified in sample problems

    erg. it formatted that weirdly.
    7x*squared* - 14x
    ________________
    4x*squared* -1

    is being reduced to:

    7x
    ______
    4(x+2)
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  3. #3
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    Re: Confused on how a complex polynomial fractions are simplified in sample problems

    Quote Originally Posted by melbell View Post
    erg. it formatted that weirdly.
    7x*squared* - 14x
    ________________
    4x*squared* -1

    is being reduced to:

    7x
    ______
    4(x+2)
    Factorise the top and bottom, then cancel any common factors between them.

    \displaystyle \begin{align*} \frac{7x^2 - 14x}{4x^2 - 1} &= \frac{7x \left( x - 2 \right)}{\left( 2x - 1 \right) \left( 2x + 1 \right) } \end{align*}

    There are not any common factors, so either you have copied the question down wrong, or your book's answer is wrong.
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    Re: Confused on how a complex polynomial fractions are simplified in sample problems

    Hello, melbell!

    \text{Simplify: }\:\dfrac{\dfrac{7}{x} - \dfrac{14}{x^2}}{\dfrac{4}{x} - \dfrac{16}{x^3}}

    Multiply by \frac{x^3}{x^3}\!:\;\;\frac{x^3\left(\dfrac{7}{x} - \dfrac{14}{x^2}\right)}{x^3\left(\dfrac{4}{x} - \dfrac{16}{x^3}\right)} \;=\;\frac{7x^2-14x}{4x^2-16}

    . . . . . . . . . . =\;\frac{7x(x-2)}{4(x^2-4)} \;=\;\frac{7x(x-2)}{4(x-2)(x+2)} \;=\;\frac{7x}{4(x+2)}
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