Welcome to Westonci.ca, the ultimate question and answer platform. Get expert answers to your questions quickly and accurately. Our platform connects you with professionals ready to provide precise answers to all your questions in various areas of expertise. Get precise and detailed answers to your questions from a knowledgeable community of experts on our Q&A platform.

Simplify the rational expression. State any restrictions on the variable
n^4-10n^2+24/ n^4-9n^2+18


Sagot :

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

Answer:

The simplified form is [tex]=\frac{(n-2)(n+2)}{(n-\sqrt3)(n+\sqrt3)}[/tex]

The variable n can not be equals to [tex]\pm\sqrt3[/tex] 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.

[tex]\frac{n^4-10n^2+24}{n^4-9n^2+18}[/tex]

We can now see that both the numerator and denominator are quadratic trinomials in [tex]n^2.\[/tex]

We split the middle terms as follows;

[tex]\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}[/tex]

          [tex]=\frac{n^2(n^2-6)-4(n^2-6)}{n^2(n^2-3)-6(n^2-3)}[/tex]

          [tex]=\frac{(n^2-4)(n^2-6)}{(n^2-6)(n^2-3)}[/tex]

          [tex]=\frac{(n-2)(n+2)}{(n-\sqrt3)(n+\sqrt3)}[/tex]

which is the simplified form of given expression.

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