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Math Help - Linear Equation Q2

  1. #1
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    Linear Equation Q2

    Question
     \frac{4}{25w^2}+\frac{3}{5w-1}=\frac{2}{5w-1}

    Attempt:

     \frac{4}{(5w+1)(5w-1)}+\frac{3}{5w-1}=\frac{2}{5w-1}

     w=\frac{3}{20}

    Thank you
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  2. #2
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    \frac{4}{25w^2}+\frac{3}{5w-1}=\frac{2}{5w-1}

    \frac{4}{25w^2}=\frac{-3}{5w-1}+\frac{2}{5w-1}

    \frac{4}{25w^2}=\frac{-1}{5w-1}

    Hence

    4(5w-1)= -25w^2

    20w-4=-25w^2

    25w^2+20w-4=0
    ____________for next steps read the last lines if you don't get it_______

    <br />
w=\frac{-20\pm \sqrt{20^2-(4\times 25\times -4)}}{2\times 25}

    w=\frac{-20\pm \sqrt{400+400}}{50}

    <br />
w=\frac{20(-1+ \sqrt{2})}{50}~And~\frac{20(-1- \sqrt{2})}{50}

    w=\frac{2( \sqrt{2}-1)}{5} ~And~ \frac{-2(1+\sqrt{2})}{5}
    .................................................. .......................................

    For a quadratic equation
    ax^2 +bx+c= 0
    The two roots are \frac{-b\pm \sqrt{b^2-4ac}}{2a}
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