Question

Simplify the rational expression. State any restrictions on the variable

Answer 1

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

Answer 2

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.