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Math Help - Simplify Rational Expression with Fractional Exponents

  1. #1
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    Simplify Rational Expression with Fractional Exponents

    I'm a bit stuck on this one.

    Simplify:

    \frac{\frac{3}{x^{\frac{1}{2}}}+\frac{1}{x^{7}}} {6-\frac{2}{x}}<br />
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  2. #2
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    Why does the exponent type change anything. Just proceed as usual.

    Add fractions by finding a common denominator. \frac{3}{x^{\frac{1}{2}}}+\frac{1}{x^7}\;=\;\frac{  3\cdot x^{\frac{13}{2}}+1}{x^7}
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  3. #3
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    You can also begin by multiplying each term by x^7. This will turn the complex fraction into a simple fraction.
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  4. #4
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    Ok. So the common denominator for the top is x^(13/2) because the base x remains the same and the exponents are added together. So that give x^14/2 which is the same as x^7.
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  5. #5
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    I think I'm on the wrong path here:

    \frac{3x^{\frac{15}{2}}+x}{6x^{8}-2x^{7}}
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  6. #6
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    What you have is actually correct. I'm just not sure why you multiplied each term by x^8 instead of x^7.
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  7. #7
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    I just encountered another problem that is very similar to the one I've been having trouble with. All I got to do is simplify it. It seems that whatever I try leads me to the wrong answer. I would appreciate if someone can show me step by step how to handle this type of problem. Thanks

    This is an image of where I get stuck:

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  8. #8
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    Dividing each term by x just makes the fraction more complicated. You want to multiply each term by x^8.

    Note that x^{-8}=\frac{1}{x^8}.
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  9. #9
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    I know that I need to divide by x because I'm using coursecompass and it shows to do that. The other steps are skipped. I'm trying to find the limit of that function as x approaches infinity. I'm stuck on the algebra of something that shouldn't take me more than a few minutes to figure out. That's why I was requesting a step by step show of the algebra because that's what coursecompass is skipping.

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  10. #10
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    You didn't say you were taking a limit. Just take the highest power of x on top and on bottom, divide and take the limit:

    \frac{5\sqrt{x}}{7x}=\frac{5}{7\sqrt{x}}. This approaches 0.
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  11. #11
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    I know I didn't mention I was taking a limit because I thought all I had to do was simplify and then evaluate. I realized soon after my last post that after dividing the expression by the highest power of x (which is just x in this case), I then evaluate. Thanks anyway for the help.
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  12. #12
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    Dividing by the highest power of x is not simplifying the complex fraction. But it is the best way to evaluate the limit.
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