Question

Solve n^4-11n^2+30÷n^4-7n^2+10

Answer 1

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)