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

Question

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

parthkohli · Answer

You have to factor the numerator and denominator. For that, you can do algebraic substitution. 

Start with the numerator:
Let $n^2 = y$, then we have $y^2 - 10y + 24$... factor this quadratic expression.

Same for the denominator:
Let $n^2 = y$, then we have $y^2 - 9n + 18$

parthkohli · Answer

For the restrictions, the denominator can't be zero, so the restriction is the following:$$y^2 - 9n + 18 = 0$$Solve for $y$, then square it to solve for $n^2$.

parthkohli · Answer

Actually, find the square root of $y$ to solve for $n$.

anonymous · Answer

$$\frac{ (y-6)(y-4)}{ (y-3)(y-6) }$$