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Math Help - Complex Fractions help.

  1. #1
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    Complex Fractions help.

    Not sure how to write this out...

    {(8/x+y)+1/4}/{(x/x+y)-1}

    My converter says it should be written like

    @DIV{@DIV{8;x+y}+@DIV{1;4};@DIV{x;x+y}-1} If that help. PLZ if you help show steps so I can figure out how to do this correctly.
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  2. #2
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    Re: Complex Fractions help.

    Quote Originally Posted by selfadmrier View Post
    Not sure how to write this out...

    {(8/x+y)+1/4}/{(x/x+y)-1}

    My converter says it should be written like

    @DIV{@DIV{8;x+y}+@DIV{1;4};@DIV{x;x+y}-1} If that help. PLZ if you help show steps so I can figure out how to do this correctly.
    First, it appears that you are not using parentheses to state your problem correctly. Second, I have no clue what you mean by a converter.

    Is this your problem

    $Simplify\ \left(\dfrac{8}{x + y} + \dfrac{1}{4}\right) \div \left(\dfrac{x}{x + y} - 1\right).$

    If so, the first step is to change each expression in parentheses into a single fraction. What do you get for each one?

    Now when you divide a fraction by a fraction, how do you proceed?

    So now what do you have?

    And that simplifies nicely to what?
    Thanks from topsquark
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  3. #3
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    Re: Complex Fractions help.

    My problem seems to be getting the 2 fractions to one, Which should be easy right..

    32+x+y/4(x+y) the second I get -y/x+1

    flip the 2nd and multiply x^2+33x+xy+y+32/-4y(x+y)

    But It's not right of course.. I just can't put my finger on what I am doing wrong.
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  4. #4
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    Re: Complex Fractions help.

    Quote Originally Posted by selfadmrier View Post
    My problem seems to be getting the 2 fractions to one, Which should be easy right..

    (32+x+y)/(4(x+y)) Be careful with parentheses when writing in line

    the second I get -y/x+1 This is wrong: see below

    flip the 2nd and multiply x^2+33x+xy+y+32/-4y(x+y)

    But It's not right of course.. I just can't put my finger on what I am doing wrong.
    $Simplify\ \left(\dfrac{8}{x + y} + \dfrac{1}{4}\right) \div \left(\dfrac{x}{x + y} - 1\right).$

    First step: get common denominators

    $\left(\dfrac{8}{x + y} + \dfrac{1}{4}\right) \div \left(\dfrac{x}{x + y} - 1\right) = \left(\dfrac{4 * 8}{4 * (x + y)} + \dfrac{1 * (x + y)}{4 * (x + y) }\right) \div \left(\dfrac{x}{x + y} - \dfrac{x + y}{x + y}\right).$

    Second step: add fractions

    $\left(\dfrac{4 * 8}{4 * (x + y)} + \dfrac{1 * (x + y)}{4 * (x + y) }\right) \div \left(\dfrac{x}{x + y} - \dfrac{x + y}{x + y}\right) = \dfrac{32 + x + y}{4(x + y)} \div \left(-\ \dfrac{y}{x + y}\right).$

    Third step: "flip" divisor

    $\dfrac{32 + x + y}{4(x + y)} \div \left(-\ \dfrac{y}{x + y}\right) = \dfrac{32 + x + y}{4(x + y)} * \left(-\ \dfrac{x + y}{y}\right).$

    Fourth step: Multiply and simplify

    $\dfrac{32 + x + y}{4(x + y)} * \left(-\ \dfrac{x + y}{y}\right) = -\ \dfrac{(32 + x + y)(x + y)}{4y(x + y)} = -\ \dfrac{32 + x + y}{4y}.$
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  5. #5
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    Re: Complex Fractions help.

    Hello, selfadmrier!

    \text{Simplify: }\: \dfrac{\dfrac{8}{x+y} + \dfrac{1}{4}}{\dfrac{x}{x+y} - 1}

    Multiply top and bottom by the LCD of all the denominators.
    This would be: 4(x+y)


    \dfrac{4(x+y)\cdot \left(\dfrac{8}{x+y} + \dfrac{1}{4}\right)} {4(x+y)\cdot\left(\dfrac{x}{x+y} - 1\right)} \;\;=\;\;\dfrac{4(x+y)\cdot\dfrac{8}{x+y} + 4(x+y)\cdot\dfrac{1}{4}} {4(x+y)\cdot\dfrac{x}{x+y} - 4(x+y)\cdot 1}


    . . =\;\;\frac{32 + x + y}{4x - 4x - 4y} \;\;=\;\;\frac{32+x+y}{-4y}
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