[tex]\bf \textit{difference of squares}
\\\\
(a-b)(a+b) = a^2-b^2\qquad \qquad
a^2-b^2 = (a-b)(a+b)\\\\
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\cfrac{2x+4}{x^2-4}+\cfrac{x+3}{x^2+5x+6}\implies \cfrac{2(x+2)}{x^2-2^2}+\cfrac{\underline{x+3}}{\underline{(x+3)}(x+2)}[/tex]
[tex]\bf \cfrac{2\underline{(x+2)}}{(x-2)\underline{(x+2)}}+\cfrac{1}{x+2}\implies \cfrac{2}{x-2}+\cfrac{1}{x+2}\impliedby \stackrel{LCD}{(x-2)(x+2)}
\\\\\\
\cfrac{2(x+2)~~+~~1(x-2)}{(x-2)(x+2)}\implies \cfrac{2x+4+x-2}{(x-2)(x+2)}\implies \cfrac{3x+2}{(x-2)(x+2)}
\\\\\\
\cfrac{3x+2}{x^2-2^2}\implies \cfrac{3x+2}{x^2-4}[/tex]
