lizziepagan17 lizziepagan17
  • 21-10-2017
  • Mathematics
contestada

How do I write this as a single rational expression?

[tex] \frac{1}{p-2} - \frac{1}{p+2} [/tex]

Respuesta :

jdoe0001 jdoe0001
  • 21-10-2017
[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)\\\\ -------------------------------\\\\ \cfrac{1}{p-2}-\cfrac{1}{p+2}\impliedby \textit{so let's use the }\stackrel{LCD}{(p-2)(p+2)} \\\\\\ \cfrac{(p+2)~~-~~(p-2)}{(p-2)(p+2)}\implies \cfrac{\underline{p}+2~~\underline{-p}+2}{(p-2)(p+2)}\implies \cfrac{4}{p^2-2^2}\implies \cfrac{4}{p^2-4}[/tex]
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