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what is the difference in simplest form? [tex] \frac{n^2+3n+2}{n^2+6n+8}-\frac{2n}{n+4} [/tex]


First picture example problem
Second picture problem with the answers.

what is the difference in simplest form tex fracn23n2n26n8frac2nn4 tex First picture example problem Second picture problem with the answers class=
what is the difference in simplest form tex fracn23n2n26n8frac2nn4 tex First picture example problem Second picture problem with the answers class=

Respuesta :

[tex]\bf \cfrac{n^2+3n+2}{n^2+6n+8}-\cfrac{2n}{n+4}\implies \cfrac{n^2+3n+21}{(n+4)(n+2)}-\cfrac{2n}{n+4} \\\\\\ \textit{so our LCD will just be (n+4)(n+2)} \\\\\\ \cfrac{n^2+3n+2~~~~-~~~~(n+2)(2n)}{(n+4)(n+2)} \\\\\\ \cfrac{n^2+3n+2~~~~-~~~~(2n^2+4n)}{(n+4)(n+2)} \\\\\\ \cfrac{n^2+3n+2~~~~-~~~~2n^2-4n}{(n+4)(n+2)} \implies \cfrac{-n^2-n+2}{(n+4)(n+2)} \\\\\\ \cfrac{-(n^2+n-2)}{(n+4)(n+2)}\implies \cfrac{-\underline{(n+2)}(n-1)}{(n+4)\underline{(n+2)}}\implies \cfrac{-(n-1)}{n+4}\implies \cfrac{1+n}{n+4}[/tex]

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