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Math Help - Complex Fraction Help

  1. #1
    Junior Member fluffy_penguin's Avatar
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    Red face Complex Fraction Help

    Can someone help me in detail showing their steps to get the answer to this problem:

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  2. #2
    Math Engineering Student
    Krizalid's Avatar
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    Here's a Hint:

    \frac{{y - \dfrac{{5y - 7}}<br />
{7}}}<br />
{{\dfrac{6}<br />
{{14}} + \dfrac{3}<br />
{{2y}}}} = \frac{{14\left( {y - \dfrac{{5y - 7}}<br />
{7}} \right)}}<br />
{{14\left( {\dfrac{6}<br />
{{14}} + \dfrac{3}<br />
{{2y}}} \right)}}.

    Can you see that it is easier now?
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  3. #3
    Junior Member fluffy_penguin's Avatar
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    Not really, no. > >

    I see where you got the 14 from since it's the lcd but I've no clue what to do next.
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  4. #4
    Super Member

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    Hello, fluffy_penguin!

    Use any method to simplify the complex fraction.

    \frac{y - \frac{5y-7}{7}}{\frac{6}{14} - \frac{3}{2y}}

    Multiply top and bottom by the LCD, 14y

    \frac{14y\left(y - \frac{5y-7}{7}\right)}{14y\left(\frac{6}{14} - \frac{3}{2y}\right)} \;=\;\frac{14y\cdot y \:- \:14y\cdot\frac{5y-7}{7}}{14y\cdot\frac{6}{14} \:- \:14y\cdot\frac{3}{2y}} \;= \;\frac{14y - 2y(5y-7)}{6y - 7\cdot3}

    . . =\;\frac{14y^2 - 10y^2 + 14y}{6y-21} \;= \;\frac{4y^2+14y}{6y-21} \;=\;\frac{2y(2y + 7)}{3(2y-7)}

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