Question

Simplify the rational expression. State any restrictions on the variable.

Answer 1

\[\frac{ n ^{4}-10n ^{2}+24 }{ n ^{4}-9n ^{2}+18 }\]

Answer 2

@jim_thompson5910

Answer 3

\[\Large n^{4}-10n^{2}+24\]

partially factors to

\[\Large (n^2-6)(n^2-4)\]

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\[\Large n^{4}-9n^{2}+18\]

factors to

\[\Large (n^2-6)(n^2-3)\]

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so

\[\Large \frac{ n ^{4}-10n ^{2}+24 }{ n ^{4}-9n ^{2}+18 }\]

is the same as

\[\Large \frac{ (n^2-6)(n^2-4) }{ (n^2-6)(n^2-3) }\]

Answer 4

so dont the n^2 - 6 divide out?

Answer 5

the n^2 - 6 terms will cancel, good

Answer 6

leaving you with

\[\Large \frac{n^2-4 }{ n^2-3 }\]

Answer 7

@jim_thompson5910 what are the restrictions though?

Answer 8

would it be 6 and -3?

Answer 9

basically n can't equal sqrt(6), -sqrt(6), sqrt(3), -sqrt(3)

those 4 values make the denominator equal to zero, so they are the restrictions

Answer 10

its either