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 can factor the numerator and the denominator.
The numerator factors as:
n^4 - 11n^2 + 30 = (n^2 - 6)(n^2 - 5)
The denominator factors as:
n^4 - 7n^2 + 10 = (n^2 - 2)(n^2 - 5)
Now we can simplify further by canceling out the common factor of (n^2 - 5), leaving us with:
(n^2 - 6)/(n^2 - 2)
The restrictions on the variable occur when the denominator is equal to zero. So, we need to solve the equation (n^2 - 2) = 0. Solving this equation, we find that n = ±√2.
Therefore, the simplified rational expression is (n^2 - 6)/(n^2 - 2), with the restriction that n is not equal to ±√2.