Simplify the rational expression. State any restrictions on the variable n^4-11n^2+30/ n^4-7n^2+10

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]