Question

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

Answer 1

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