Answer:
The simplified form is \(=\frac{(n-2)(n+2)}{(n-\sqrt3)(n+\sqrt3)}\)
The variable n can not be equals to \(\pm\sqrt3\) as for these value denominator equals to zero which becomes an indeterminate form.
Step-by-step explanation:
we have to simplify the rational expression and state the restrictions on the variable.
\(\frac{n^4-10n^2+24}{n^4-9n^2+18}\)
We can now see that both the numerator and denominator are quadratic trinomials in \(n^2.\\)
We split the middle terms as follows;
\(\frac{n^4-10n^2+24}{n^4-9n^2+18}=\frac{n^4-6n^2-4n^2+24}{n^4-3n^2-6n^2+18}\)
\(=\frac{n^2(n^2-6)-4(n^2-6)}{n^2(n^2-3)-6(n^2-3)}\)
\(=\frac{(n^2-4)(n^2-6)}{(n^2-6)(n^2-3)}\)
\(=\frac{(n-2)(n+2)}{(n-\sqrt3)(n+\sqrt3)}\)
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.
