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Math Help - Complex fraction

  1. #1
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    Complex fraction

    I am not sure if i entered this correctly


    <br />
\frac {{ab+b^2}{4ab^5}}{{a+b}{6a^2b^4}}<br />
    Last edited by CaptainBlack; July 31st 2006 at 10:55 PM.
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  2. #2
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    Quote Originally Posted by Chester
    I am not sure if i entered this correctly


    math]
    \frac {{ab+b^2}{4ab^5}}{{a+b}{6a^2b^4}}
    [/tex]
    maybe you're trying to say:
    <br />
\frac{\frac{ab+b^2}{4ab^5}}{\frac{a+b}{6a^2b^4}}<br />
    but that seems silly, with the bracket you left out your expression is:
    <br />
\frac {{ab+b^2}{4ab^5}}{{a+b}{6a^2b^4}}<br />
    but I don't understand...
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  3. #3
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    Another try

    <br />
\frac{ \frac{ab+b^2}{4ab^5} }{ \frac{a+b}{6a^2b^4}}<br />
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  4. #4
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    Quote Originally Posted by Chester
    <br />
\frac{ \frac{ab+b^2}{4ab^5} }{ \frac{a+b}{6a^2b^4}}<br />
    now you're going to need to clarify, are you saying:

    \frac{ab+b^2}{4ab^5} \div \frac{a+b}{6a^2b^4}
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  5. #5
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    Clarification

    Sorry,
    I was trying to get the code to work. That is what i am saying. I have to simplify and reduce.

    Thanks
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  6. #6
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    Another try

    Rational expressions

    I have to simplify and reduce the following

    <br />
\frac{ \frac{ab+b^2}{4ab^5} }{ \frac{a+b}{6a^2b^4}}<br />

    Chester
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  7. #7
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    Quote Originally Posted by Chester
    Sorry,
    I was trying to get the code to work. That is what i am saying. I have to simplify and reduce.

    Thanks
    <br />
\frac{ab+b^2}{4ab^5} \div \frac{a+b}{6a^2b^4}<br />
    switch the division sign to multiplication: \frac{ab+b^2}{4ab^5} \times \frac{6a^2b^4}{a+b}

    multiply: \frac{(ab+b^2)(6a^2b^4)}{(4ab^5)(a+b)}

    seperate: \frac{ab+b^2}{a+b} \times \frac{6a^2b^4}{4ab^5}

    divide: \frac{ab+b^2}{a+b} \times \frac{6a}{4b}

    multiply: \frac{6a(ab+b^2)}{4b(a+b)}

    multiply: \frac{6a^2b+6b^2a}{4ab+4b^2}

    split: \frac{6a^2b}{4ab+4b^2}+\frac{6b^2a}{4ab+4b^2}

    simplify: \frac{6a^2b}{4b(b+a)}+\frac{6b^2a}{4b(b+a)}

    simplify: \frac{3a^2}{2(b+a)}+\frac{3ab}{2(b+a)}

    add: \frac{3a^2+3ab}{2(b+a)}

    combine: \frac{3a(a+b)}{2(b+a)}

    seperate: \frac{3a}{2}\times\frac{a+b}{b+a}

    simplify: \frac{3a}{2}\times1

    simplify: \frac{3a}{2}

    I might have done more work than necessary, but I got the job done...
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  8. #8
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    shorter "quicker" work

    Quote Originally Posted by Quick
    switch the division sign to multiplication: \frac{ab+b^2}{4ab^5} \times \frac{6a^2b^4}{a+b}

    multiply: \frac{(ab+b^2)(6a^2b^4)}{(4ab^5)(a+b)}

    seperate: \frac{ab+b^2}{a+b} \times \frac{6a^2b^4}{4ab^5}
    simplify: \frac{b(a+b)}{a+b} \times \frac{6a}{4b}

    simplify: b \times \frac{3a}{2b}

    multiply: \frac{3ab}{2b}

    simplify: \frac{3a}{2}
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  9. #9
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    Lcd

    I would like to solve this by finding the LCD and simplifying.

    I think the LCD will be 12a^2b^5

    Is that the corect start?
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  10. #10
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    Quote Originally Posted by Chester
    I would like to solve this by finding the LCD and simplifying.

    I think the LCD will be 12a^2b^5

    Is that the corect start?
    Yes, that will work.

    -Dan
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  11. #11
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    Quote Originally Posted by Chester
    I would like to solve this by finding the LCD and simplifying.

    I think the LCD will be 12a^2b^5

    Is that the corect start?
    division and multiplication doesn't require an LCD
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  12. #12
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by Quick
    division and multiplication doesn't require an LCD
    No, it isn't required, but the standard method to simplify a complex fraction is to multiply the numerator and denominator by the LCD of the denominators of the "lesser" fractions. (I'm not sure what the standard terminology is here.) You can, of course, use other methods.

    -Dan
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