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Thread: Simplifying complex fraction

  1. #1
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    Simplifying complex fraction

    I know I shoudl know this, but it's late and for some reason I am drawing a blank. Any help would be appreciated. Thanks

    How does $\displaystyle \frac{\frac{3}{x}}{1+\frac{4}{x^2}}$ simplify to $\displaystyle \frac{3x}{x^2+4}$
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  2. #2
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    Hello, dbakeg00!

    $\displaystyle \text{How does }\,\dfrac{\frac{3}{x}}{1+\frac{4}{x^2}}\,\text{ simplify to }\,\dfrac{3x}{x^2+4}$

    Multiply by $\displaystyle \dfrac{x^2}{x^2}$

    . . $\displaystyle \displaystyle \frac{x^2}{x^2}\cdot \frac{\frac{3}{x}}{1+\frac{4}{x^2}} \;=\;
    \dfrac{x^2\left(\frac{3}{x}\right)}{x^2\left(1 + \frac{4}{x^2}\right)} \;=\;\frac{3x}{x^2+4} $

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  3. #3
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    Thanks for the help. I know I need to go to bed when I start struggling with something like this!
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