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Math Help - Can I simply e^3x/e^2x ?

  1. #1
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    Can I simply e^3x/e^2x ?

    If I have:

    y = \frac{e^3x + 4}{e^2x}

    Can I simply as you would eg with x^3/x^2?

    Can I call it:

    y = e^x + \frac{4}{e^2x}

    What are the rules in simplifying these? Or can you not?

    Angus
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  2. #2
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    Re: Can I simply e^3x/e^2x ?

    Quote Originally Posted by angypangy View Post
    If I have:

    y = \frac{e^3x + 4}{e^2x}

    Can I simply as you would eg with x^3/x^2?

    Can I call it:

    y = e^x + \frac{4}{e^2x}

    What are the rules in simplifying these? Or can you not?

    Angus
    1. I assume that you mean y = \frac{e^{3x} + 4}{e^{2x}}

    2. Re-write the RHS as a product

    y = \frac{e^{3x} + 4}{e^{2x}}=\left( e^{3x} + 4 \right) \cdot \frac1{e^{2x}}

    3. Expand the RHS and cancel equal factors:

    \left( e^{3x} + 4 \right) \cdot \frac1{e^{2x}} = \frac{e^{3x}}{e^{2x}} + \frac4{e^{2x}}
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  3. #3
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    Re: Can I simply e^3x/e^2x ?

    Or write it as: \left(e^{3x}+ 4\right)e^{-2x}= e^{3x- 2x}+ 4e^{-2x}= e^{x}+ 4e^{-2x}.
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  4. #4
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    Re: Can I simply e^3x/e^2x ?

    Quote Originally Posted by HallsofIvy View Post
    Or write it as: \left(e^{3x}+ 4\right)e^{-2x}= e^{3x- 2x}+ 4e^{-2x}= e^{x}+ 4e^{-2x}.
    That's what I thought but I put both into my TI calculator and it seemed to give different graphs. I must have done something wrong because they are the same now.
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