226k views
4 votes
Simplify the rational expression. State any restrictions on the variable

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

2 Answers

6 votes
The answer to the question is n^2-4/n^2-3 n ≠±√6±√3
User Steve McGuire
by
10.1k points
2 votes

Answer:

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.

User Ahnbizcad
by
8.9k points