how would this problem be simplifyed?

Question

the problem is:
x^2+x^3+x^4/x^-2+x^-3+x^-4

Answer 1

Do you mean:

(x^2+x^3+x^4)/(x^-2+x^-3+x^-4)?

If so:

(x^4+x^3+x^2)/[1/(x^2)+1/(x^3)+(1/x^4)]

Let's work with 1/(x^2)+1/(x^3)+(1/x^4) real quick:
x^2/x^4+x/x^4+1/x^4=(x^2+x+1)/x^4

So: (x^4+x^3+x^2)/[(x^2+x+1)/x^4] = (x^4)(x^4+x^3+x^2)/(x^2+x+1) =
(x^6)(x^2+x+1)/(x^2+x+1)=x^6

x^6 is the most simplified you can go.

Answer 2

All the terms in the numerator have an x in them -- in fact, they all have an x^2. So you can take out that term, giving you x^2(1+x+x^2). The usual way to write what's inside the parentheses is (x^2+x+1).

In the denominator, all the terms also have a power of x. You can take out x^-2, so the denominator is x^-2(1+x^-1+x^-2).

Now you have to clean up the denominator. x^-2 is 1/x^2, so if you multiply both numerator and denominator by x^2, you have x^4 in the numerator and 1 in the denominator.

So far, your fraction is x^4(x^2+x+1) / (x^-2+x^-1+1).

Still not done -- there's a mess in the denominator. You can rewrite that as

1/x^2 + 1/x +1.

You need a common denominator to combine those terms; x^2 will work. So you now have 1/x^2 + x/x^2 + x^2/x^2. Add those up, and you have (reversing the order) x^2 + x + 1/x^2.

That looks promising. To get rid of the fraction in the denominator, invert and multiply, and it looks like the trinomial will cancel.

So after you cancel the trinomial, you have x^4 times x^2, or x^6. Pretty simple answer from a messy beginning.

Answer 3

x^2 + x^3 +x^6 +x^-3 +x^-4

that is as simplified as it gets the way you wrote your question. The only term that need simplification was the x^4/x^-2 term.
to simplify it you just subtract the degree of the denominator from the degree of the numerator, (4 - -2 = 6) .

Since there are no terms with the same degree you cannot combine any of these terms.


something inside me tells me that you meant to write: (x^2+x^3+x^4) / (x^-2+x^-3+x^-4)

You must remember to use parenthesis in the explanations of your homework problems. The answer in this case is actually pretty complicated.

Answer 4

X^9/X^-9

Answer 5

i'll pray 4 u