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Math Help - Simplifying a rational function

  1. #1
    Member nautica17's Avatar
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    Simplifying a rational function

    I made this random problem:

    ((x^-7)(y^2)) / ((x^-3) + y^-4))

    and I'm trying to simplify it.

    So I've gotten down to this:

    ((x^3)(y^6)) / ((y^4)(x^7)) + x^10)

    and I guess this could technically be an acceptable answer but when I punched this into my calculator, I got it simplified to:

    (y^6) / ((x^4)(y^4) + x^7)

    Can someone show me (with steps please) how to get that final result.

    Thank-you!
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  2. #2
    Master Of Puppets
    pickslides's Avatar
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    can you confirm this is the expression?

     \frac{x^{-7}y^2}{x^{-3}+y^{-4}}

    If so

     \frac{y^2}{x^7(x^{-3}+y^{-4})}

    expanding the denominator

     \frac{y^2}{(x^{4}+x^7y^{-4})}

    It can't get much simplier than this.
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  3. #3
    Member nautica17's Avatar
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    Yup that was the original function.

    Cool thank-you. That makes solving it a lot simpler actually. I was doing things the long way.
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  4. #4
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    Smile

    \frac{y^2}{x^7\left ( \frac{1}{x^3}+\frac{1}{y^4} \right )}=\frac{y^2}{x^7x^-3+x^7y^-4}=\frac{y^2}{x^4+x^7y^-4} multiply the denominator and the nominator by  y^4
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