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Math Help - newby needing to know how to combine a natural number and an algebraic fraction

  1. #1
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    newby needing to know how to combine a natural number and an algebraic fraction

    Im new to algebra and need to know how:

    1 + 2/x^2 + 4 can be combined into 1 term

    thanks
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  2. #2
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    e^(i*pi)'s Avatar
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    Re: newby needing to know how to combine a natural number and an algebraic fraction

    Quote Originally Posted by ahdavewest751 View Post
    Im new to algebra and need to know how:

    1 + 2/x^2 + 4 can be combined into 1 term

    thanks
    Are you familiar with adding numerical fractions? If so you know that to add fractions we need to have a common denominator.

    Spoiler:
    For example \dfrac{2}{3} + \dfrac{1}{7} = \dfrac{2}{3} \times \dfrac{7}{7} + \dfrac{1}{7} \times \dfrac{3}{3} = \dfrac{14}{21} + \dfrac{3}{21} = \dfrac{17}{21}. For integers (whole numbers) you learned that you multiply top and bottom but whatever suited.


    First you may as well say that 1+4 = 5 to make our life easier

    It is the same principle with algebra, you want to get it so that 5 \text{  and  }\dfrac{2}{x^2} have the same denominator. So what would you multiply \dfrac{5}{1} by to get a common denominator?
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  3. #3
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    Re: newby needing to know how to combine a natural number and an algebraic fraction

    ok so I tried this:

    1 + 2/x^2 + 4 =

    1/x^2 + 4 + 2/x^2 + 4 =

    then multiplied the top left numerator by the bottom right denominator and added the numerator to get:

    x^2 + 6/x^2 + 4

    is that the way its done?
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  4. #4
    Super Member Quacky's Avatar
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    Re: newby needing to know how to combine a natural number and an algebraic fraction

    I'm extremely confused. Is it:

    1+\frac{2}{x^2}+4, or:

    1+\frac{2}{x^2+4}

    The lack of brackets implies the former; your working out (and logic) implies the latter is actually the case, however.
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  5. #5
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    Re: newby needing to know how to combine a natural number and an algebraic fraction

    Check out
    http://www.mathhelpforum.com/math-he...orial-266.html
    for info on how to make fractions look nice.

    But given:
    1+\frac{2}{x^2+4}
    you are correct.

    \frac{1}{1}*\frac{x^2+4}{x^2+4}+\frac{2}{x^2+4} =

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

    \frac{x^2+6}{x^2+4}
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