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\title{From Algebra to Algebraic Structures}
\author{Mathematics 43, section 1}

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\samepage \begin{displaymath}\frac{\frac{a}{b}+\frac{c}{d}}{e}=\frac{ad+bc}{bde}\end{displaymath}
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\samepage \begin{displaymath}ax^2+bx+c=a\left(x^2+\frac{b}{a}x+\frac{c}{a}\right)\end{displaymath}
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\samepage \begin{displaymath}=a\left(\left(x+\frac{b}{2a}\right)^2+\frac{4ac-b^2}{4a^2}\right)\end{displaymath}
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\samepage \begin{displaymath}\left(x+\frac{b}{2a}\right)^2=\frac{b^2-4ac}{4a^2}. \end{displaymath}
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\samepage \begin{displaymath}x+\frac{b}{2a}=\pm\sqrt{\frac{b^2-4ac}{4a^2}}. \end{displaymath}
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\samepage \begin{displaymath}x=\frac{-b}{2a}\pm\sqrt{\frac{b^2-4ac}{4a^2}}\end{displaymath}
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\samepage \begin{displaymath}x=\frac{-b}{2a}\pm\frac{\sqrt{b^2 - 4ac}}{2a}=\frac{-b\pm\sqrt{b^2-4ac}}{2a}\end{displaymath}
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