For this case we have the following expression:
[tex] \frac{n ^ 4-11n ^ 2 + 30}{ n ^ 4-7n ^ 2 + 10}
[/tex]
We are going to make the following change of variables:
[tex]x = n ^ 2
[/tex]
Rewriting the expression we have:
[tex] \frac{(x ^ 2-11x + 30)}{(x ^ 2-7x + 10)}
[/tex]
Factoring the expression we have:
[tex] \frac{(x-5) (x-6)}{(x-5) (x-6)}
[/tex]
Canceling similar terms we have:
[tex] \frac{x-6}{x-2}
[/tex]
Returning the change we have:
[tex] \frac{n ^ 2-6}{n ^ 2-2}
[/tex]
The resctrictions of the function are those that make the denominator equal to zero.
We have then:
[tex]n ^ 2-2 = 0
n = +/- \sqrt{2}
[/tex]
Answer:
The simplified expression is:
[tex] \frac{n ^ 2-6}{n ^ 2-2} [/tex]
The restrictions are:
[tex] n = \sqrt{2}
[/tex]
[tex]n = - \sqrt{2} [/tex]
