Solve n^4-11n^2+30:n^4-7n^2+10

Factor the numerator and denominator ...

(n^4-5n^2-6n^2+30) / (n^4-2n^2-5n^2+10)

[n^2 (n^2-5) - 6 (n^2-5) ]/[n^2 (n^2-2) - 5 (n^2-2) ]

[ (n^2-5) (n^2-6) ]/[ (n^2-5) (n^2-2) ] notice the (n^2-5) s cancel out

(n^2-6) / (n^2-2)

We could further factor this because each is a difference of squares to:

[ (n+√6) (n-√6) ]/[ (n+√2) (n-√2)