simplify the rational expression. state any restrictions on the variable. (n^4 - 11n^2 + 30)/(n^4 - 7n^2 + 10)
To simplify the rational expression (n^4 - 11n^2 + 30)/(n^4 - 7n^2 + 10), we need to factor the numerator and denominator.
(n^4 - 11n^2 + 30) factors into (n^2 - 6)(n^2 - 5)
(n^4 - 7n^2 + 10) factors into (n^2 - 2)(n^2 - 5)
Therefore, the rational expression simplifies to (n^2 - 6)/(n^2 - 2).
The restrictions on the variable are n cannot equal ±√2 and n cannot equal ±√5.