Question

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

Answer 1

Consider y=n^2, then the expression simplifies to \[ \frac{(y^2-10y+24)}{(y^2-9y+18)} \]
which can be readily factorized.
Any common factor (such as (y-6)) can be cancelled provided that we specify the restriction that (y-6) \( \ne \) 0, or equivalently \(n^2 \ne 0 \), or \( n \ne 0\). The factors that are left will be the answer.

Answer 2

@mathmate i have no clue what you just did this is my first day of algebra 2 and i barely passes alegbra 1 and prealgebra

Answer 3

Have you done quadratic equations and factorization?

Answer 4

honestly no ive tried but always failed at doing them correctly

Answer 5

Math is a cumulative subject. If you have not mastered the foundation, you cannot proceed further.

I suggest you go back and learn or relearn the basics, or else you will be struggling all the time.

This problems requires the following techniques:
1. substitution of one variable for another (to simplify the expression)
2. factorization of a quadratic equation.
3. cancellation of common factors while specifying a restriction.

I think you are in the process of learning #3, which requires a prior knowledge of #1 and #2. Passing prealgebra and algebra 1 does not make it easy for your algebra 2 course if you have not actually master the topics of the previous courses. I suggest you go back and review your prealgebra and algebra 1 or else you will fall way behind in your algebra 2 course.

It is easy for me to give you the answer, but it will just help you fall behind further.

Answer 6

wow

Answer 7

i guess ill have to guess on that question then thats for trying to help.

Answer 8

thanks not thats

Answer 9

Thank or no thanks does not matter for me. What is important for me is you learn your basics so you can continue your algebra 2 course correctly.
I am willing to give you a detailed example for the process, but you will need to work out the answers for this particular problem. This is the rule of this forum anyway.
Would you like to see a detailed example?

Answer 10

if you can put it into really simple steps yes lol

Answer 11

ok.
Here's an example:
simplify \[ \frac{x^2+2x+1}{x^2-1} \]

You probably still remember that \( x^2+2x+1=(x+1)^2 \) and \( x^2-1=(x+1)(x-1)\).
So the expression can be written as:
\[ \frac{(x+1)(x+1)}{(x+1)(x-1) } \]
(x+1) being a common factor in both the numerator and denominator, we could cancel it as we could do in a numerical fraction such as :
\[ \frac{5*3}{5*7} = \frac{3}{7}\]
as long as 5 does not equal zero (which is obvious).
However, since x is not known, we do not know if x+1=0, so in order to cancel the common factor (x+1), we need to specify the restriction that \(x+1\ne 0\), which is the same as \(x\ne -1\).
So the answer to the above example is:
\[ \frac{x+1}{x-1} \] as long as \(x\ne -1\)

You can solve your problem in very much the same way, but you will need to factorize the expressions in the numerator and denominator. They happen to be quite easy to factorize.