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:

`(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:

`((x ^ 2-11x + 30))/((x ^ 2-7x + 10))`
Factoring the expression we have:

`((x-5) (x-6))/((x-5) (x-6))`
Canceling similar terms we have:

`(x-6)/(x-2)`
Returning the change we have:

`(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 = +/- √(2)`
Answer:
The simplified expression is:

`(n ^ 2-6)/(n ^ 2-2)`
The restrictions are:

`n = √(2)`

`n = - √(2)`