Simplify the rational expression. State any restrictions on the variable.

Question

asked Nov 17, 2019 94.6k views

1 Answer

Tquadrat · Answer 1 · 2019-11-21T14:03:35+0000

we are given

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

Firstly, we will factor numerators and denominators

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

we can see that

n^2 -6 is factor on both numerator and denominator

so, it will get cancelled

and n^2 -6 can not be equal to 0

so, one of restriction is

$n^2-6\\eq 0$

$n\\eq -+ √(6)$

we can simplify it

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

we know that denominator can not be zero

$n^2-3\\eq 0$

$n\\eq -+ √(3)$

so, option-B.......Answer