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, we can factor the numerator and denominator.
The numerator, n^4 - 11n^2 + 30, can be factored as (n^2 - 6)(n^2 - 5).
The denominator, n^4 - 7n^2 + 10, can be factored as (n^2 - 2)(n^2 - 5).
Now, we can cancel out the common factors of (n^2 - 5) in the numerator and denominator.
The simplified rational expression is (n^2 - 6)/(n^2 - 2).
The restrictions on the variable occur when the denominator is equal to zero since division by zero is undefined.
Setting (n^2 - 2) = 0, we solve for n and find n = -√2 and n = √2.
Therefore, the restrictions on the variable are n ≠ -√2 and n ≠ √2.