Question

Medal and fan for two Algebra 2 questions.
I'll do the math, just walk me through the steps?

Simplify the rational expression and list any restrictions on the variable.

n^4-11n^2+30/n^4-7n^2+10

Answer 1

\[\frac{n^4-11n^2+30}{n^4-7n^2+10}\]

Answer 2

\[n^4-11n^2+30=n^4-5n^2-6n^2+30=n^2(n^2-5)-6(n^2-5)=\]\[(n^2-6)(n^2-5)\]

Answer 3

Factor the bottom\[n^4-7n^2+10=(n^2-5)(n^2-2)\]

Answer 4

\[\frac{(n^2-6)(n^2-5)}{(n^2-5)(n^2-2)}=\frac{n^2-6}{n^2-2}\]

Answer 5

So you.. factored yeah?

Answer 6

Solve for the restricted variable\[n^2-2=0\]\[n^2=2\]\[n=\sqrt{2},-\sqrt{2}\]

n cannot be root 2 or - root 2

Answer 7

Yes.

Factor the top, factor the bottom, and cancel out common terms.