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Math Help - HELP! Fractions, variables, exponents, THE WORKS!!

  1. #1
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    Exclamation HELP! Fractions, variables, exponents, THE WORKS!!

    (2n/n^3-5n^2) + (2/n^2+ 5n)

    Please help, i have been trying to figure this out but i cant seem to finsih it! THANKS SO MUCH
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  2. #2
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    Hello, beachchick984!

    \frac{2n}{n^3-5n^2} + \frac{2}{n^2+ 5n}

    Factor the denominators: . \underbrace{\frac{n}{n^2(n-5)}}_{\text{Reduce}} + \frac{2}{n(n+5)}

    And we have: . \frac{2}{n(n-5)} + \frac{2}{n(n+5)}

    Get a common denominator: . {\color{blue}\frac{n+5}{n+5}}\cdot\frac{2}{n(n-5)} \;+ \;{\color{blue}\frac{n-5}{n-5}}\cdot\frac{2}{n(n+5)}

    . . = \;\frac{2(n+5) + 2(n-5)}{n(n-5)(n+5)} \;= \;\frac{2n+10+2n-10}{n(n-5)(n+5)} \;=\;\frac{4n}{n(n-5)(n+5)} . =\;\boxed{\frac{4}{(n-5)(n+5)}}

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  3. #3
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    Quote Originally Posted by Soroban View Post
    Hello, beachchick984!


    Factor the denominators: . \underbrace{\frac{n}{n^2(n-5)}}_{\text{Reduce}} + \frac{2}{n(n+5)}

    And we have: . \frac{2}{n(n-5)} + \frac{2}{n(n+5)}

    Get a common denominator: . {\color{blue}\frac{n+5}{n+5}}\cdot\frac{2}{n(n-5)} \;+ \;{\color{blue}\frac{n-5}{n-5}}\cdot\frac{2}{n(n+5)}

    . . = \;\frac{2(n+5) + 2(n-5)}{n(n-5)(n+5)} \;= \;\frac{2n+10+2n-10}{n(n-5)(n+5)} \;=\;\frac{4n}{n(n-5)(n+5)} . =\;\boxed{\frac{4}{(n-5)(n+5)}}

    THANK YOU SOOOOOOOOO MUCH!!!
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  4. #4
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    Quote Originally Posted by Soroban View Post
    Hello, beachchick984!


    Factor the denominators: . \underbrace{\frac{n}{n^2(n-5)}}_{\text{Reduce}} + \frac{2}{n(n+5)}

    And we have: . \frac{2}{n(n-5)} + \frac{2}{n(n+5)}

    Get a common denominator: . {\color{blue}\frac{n+5}{n+5}}\cdot\frac{2}{n(n-5)} \;+ \;{\color{blue}\frac{n-5}{n-5}}\cdot\frac{2}{n(n+5)}

    . . = \;\frac{2(n+5) + 2(n-5)}{n(n-5)(n+5)} \;= \;\frac{2n+10+2n-10}{n(n-5)(n+5)} \;=\;\frac{4n}{n(n-5)(n+5)} . =\;\boxed{\frac{4}{(n-5)(n+5)}}
    one question when you get . =\;\boxed{\frac{4}{(n-5)(n+5)}} do you combine or finish the problem or just leave (n-5)(n+5) as is? thanks again
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