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Thread: Fraction Equalities

  1. #1
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    Fraction Equalities

    I am working on a class project on the derivation of the quadratic formula, and i understand the process of completing the square, up until the very last process of simplifying back to the quadratic forumla...

    Can someone explain how
    $\displaystyle
    -\frac{c}{a} + \frac{b^2}{4a^2} = \frac{b^2 - 4ac}{4a^2}
    $
    Last edited by nmbala; Oct 20th 2009 at 07:00 PM.
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  2. #2
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    Quote Originally Posted by nmbala View Post
    I am working on a class project on the derivation of the quadratic formula, and i understand the process of completing the square, up until the very last process of simplifying back to the quadratic forumla...

    Can someone explain how -c/a + b^2/4a^2 = (b^2 - 4ac)/4a^2
    it is just basic operation on fractions
    $\displaystyle \frac{-c}{a} + \frac{b^2}{4a^2} $
    LCM of a and$\displaystyle 4a^2$ is $\displaystyle 4a^2$
    $\displaystyle \frac{-c}{a}+ \frac{b^2}{4a^2} =\frac{{-c}\times (4a)+b^2\times 1}{4a^2} = \frac{-4ac+b^2}{4a^2}= \frac{b^2-4ac}{4a^2} $

    or you can understand it as
    multiply numerator &denominator of $\displaystyle \frac{-c}{a}$ by 4a

    $\displaystyle {\color {blue}\frac{-c}{a}}+ \frac{b^2}{4a^2} ={\color {blue}\frac{-4ac}{4a^2}}+ \frac{b^2}{4a^2} = \frac{-4ac+b^2}{4a^2}= \frac{b^2-4ac}{4a^2} $
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  3. #3
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    Quote Originally Posted by ramiee2010 View Post
    it is just basic operation on fractions
    $\displaystyle \frac{-c}{a} + \frac{b^2}{4a^2} $
    LCM of a and$\displaystyle 4a^2$ is $\displaystyle 4a^2$
    $\displaystyle \frac{-c}{a}+ \frac{b^2}{4a^2} =\frac{{-c}\times (4a)+b^2\times 1}{4a^2} = \frac{-4ac+b^2}{4a^2}= \frac{b^2-4ac}{4a^2} $

    Wow ok thx.. been a few years since ive taken a math course appears ive forgotten some of my basics of adding/subtracting fractions... Thx a bunch
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