[tex]\bf \textit{difference of squares}
\\ \quad \\
(a-b)(a+b) = a^2-b^2\qquad \qquad
a^2-b^2 = (a-b)(a+b)\\\\
-------------------------------\\\\[/tex]
[tex]\bf \cfrac{x^2}{x^2-4}-\cfrac{x+1}{x+2}\implies \cfrac{x^2}{x^2-2^2}-\cfrac{x+1}{x+2}\implies \cfrac{x^2}{(x-2)(x+2)}-\cfrac{x+1}{x+2}
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\textit{so, then the LCD will just be }(x-2)(x+2)
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\cfrac{x^2-(x+1)(x-2)}{(x-2)(x+2)}\implies \cfrac{x^2-(x^2-x-2)}{(x-2)(x+2)}\implies \cfrac{\underline{x^2-x^2}+x+2}{(x-2)(x+2)}
\\\\\\
\cfrac{\underline{x+2}}{(x-2)\underline{(x+2)}}\implies \cfrac{1}{x-2}[/tex]
