Question

Simplify the rational expression. State any restrictions on the variable

n^4-10n^2+24/ n^4-9n^2+18

Answer 1

The answer to the question is n^2-4/n^2-3 n ≠±√6±√3

Answer 2

The simplified form is
`=((n-2)(n+2))/((n-\sqrt3)(n+\sqrt3))`

The variable n can not be equals to
`\pm\sqrt3` as for these value denominator equals to zero which becomes an indeterminate form.

Explanation:

we have to simplify the rational expression and state the restrictions on the variable.

`(n^4-10n^2+24)/(n^4-9n^2+18)`

We can now see that both the numerator and denominator are quadratic trinomials in
`n^2.\`

We split the middle terms as follows;

`(n^4-10n^2+24)/(n^4-9n^2+18)=(n^4-6n^2-4n^2+24)/(n^4-3n^2-6n^2+18)`

`=(n^2(n^2-6)-4(n^2-6))/(n^2(n^2-3)-6(n^2-3))`

`=((n^2-4)(n^2-6))/((n^2-6)(n^2-3))`

`=((n-2)(n+2))/((n-\sqrt3)(n+\sqrt3))`

which is the simplified form of given expression.

The variable n can not be equals to
`\pm\sqrt3` as for these value denominator equals to zero which becomes an indeterminate form.