Simplify the rational expression. State any restriction on the variable.

Question

n^4-11n^2+30/ n^4-7n^2+10

Answer 1

To simplify the expression, we need to factor both the numerator and denominator:

n^4 - 11n^2 + 30 = (n^2 - 6)(n^2 - 5)
n^4 - 7n^2 + 10 = (n^2 - 2)(n^2 - 5)

Now we can rewrite the expression with factored terms:

((n^2 - 6)(n^2 - 5))/((n^2 - 2)(n^2 - 5))

We can cancel out the common factor (n^2 - 5) from the numerator and denominator:

(n^2 - 6)/(n^2 - 2)

So, the simplified expression is (n^2 - 6)/(n^2 - 2). The restriction on the variable is n cannot equal ±√2, as that would make the denominator zero.