Question

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

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Answer 1

you can treat this expression like a quadratic if you let u=n^2.

so you resulting equation is: \[\large \frac {u^2-11u+30}{u^2-7u+10}\]

Answer 2

factor the top and bottom, then simplify. don't forget to back substitute... :)

Answer 3

I would work on the simplification first. Both the numerator and denominator is factorable.\[n ^{4}-11n ^{2}+30 = (n ^{2}-6)(n ^{2}-5)\]
\[n ^{4}-7n ^{2}+10 = (n ^{2}-5)(n ^{2}-2)\]

Answer 4

Note that if both the numerator and denominator were divided by\[n ^{2}-5\]the fraction becomes\[n ^{2}-6 \over n ^{2}-2\] There it is simplified. But you need to find the exclusions. Division by 0 is forbidden. so the following values for n would result in a division by 0.\[n=\sqrt{5}\]
\[n=\sqrt{2}\]therefore excluded.