Simplify the rational expression. State any restrictions on the variable.
n to the fourth power minus eleven n squared plus thirty over n to the fourth power minus seven n squared plus ten
To simplify the rational expression (n^4 - 11n^2 + 30) / (n^4 - 7n^2 + 10), we need to factor the numerators and the denominators.
(n^4 - 11n^2 + 30) = (n^2 - 5)(n^2 - 6)
(n^4 - 7n^2 + 10) = (n^2 - 5)(n^2 - 2)
Now we can cancel out the common factors:
((n^2 - 5)(n^2 - 6)) / ((n^2 - 5)(n^2 - 2))
The (n^2-5) factors cancel out, and we are left with:
(n^2 - 6) / (n^2 - 2)
Therefore, the simplified expression is (n^2 - 6) / (n^2 - 2).
Restrictions on the variable:
The expression is defined for all real values of n, except when the denominator is equal to zero.
So n^2 - 2 ≠ 0, which means n ≠ ±√2.