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Math Help - Simplifying Fractions with Exponents

  1. #1
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    Simplifying Fractions with Exponents

    I understand the process of simplifying denominators but im getting stuck with questions like this. I know im trying to get to 4(x)^5/2 but how do i get there. Appreciate the help.
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  2. #2
    MHF Contributor MarkFL's Avatar
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    Re: Simplifying Fractions with Exponents

    We are given to add:

    \frac{-1}{4x^{\frac{3}{2}}}+\frac{6}{x^{\frac{5}{2}}}

    You have correctly identified the common denominator we want, although this is called the lowest common denominator:

    4x^{\frac{5}{2}}

    Now, we want to multiply both fractions by an expression equal to 1 which makes both terms have this same denominator. If you are unsure what these expressions are, take your lowest common denominator, and divide it by the existing denominators, and the result over itself is the expression we need.

    For the first term, this is \frac{4x^{\frac{5}{2}}}{4x^{\frac{3}{2}}}=x, so we multiply the first term by \frac{x}{x}.

    For the second term, this is \frac{4x^{\frac{5}{2}}}{x^{\frac{5}{2}}}=4, so we multiply the second term by \frac{4}{4}.

    Thus, we have:

    \frac{-1}{4x^{\frac{3}{2}}}\cdot\frac{x}{x}+\frac{6}{x^{ \frac{5}{2}}}\cdot\frac{4}{4}=\frac{-x}{4x^{\frac{5}{2}}}+\frac{24}{4x^{\frac{5}{2}}}

    Now, you may combine the terms.
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