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Math Help - Rational Expression Help

  1. #1
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    Rational Expression Help

    Hi,

    I am currently studying for the GMAT and came across the following problem that I seem to be having trouble understanding.

    Multiply 4X/X2 -16 x X+4/2X2

    The book I am using provides the answer but no context for getting it. Any help is much appreciated.
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  2. #2
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    Re: Rational Expression Help

    Hello, benlh1!

    \text{Simplify: }\:\frac{4x}{x^2-16} \times \frac{x+4}{2x^2}

    We have: . \frac{4x(x+4)}{2x^2(x^2-16)}

    Factor: . \frac{2\cdot2\cdot x\cdot(x+4)}{2\cdot x \cdot x(x-4)(x+4)}

    Reduce: . \frac{{\color{red}\rlap{/}}2\cdot2\cdot{\color{red}\rlap{/}}x\cdot({\color{red}\rlap{/////}}x+4)}{{\color{red}\rlap{/}}2\cdot{\color{red}\rlap{/}}x \cdot x(x-4)({\color{red}\rlap{/////}}x+4)}

    Answer: . \frac{2}{x(x-4)}
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