messed up problem, will you help?

Question

1 + (1/x) - (12/x^2) / 1+ (2/x) - (8/x^2)

Answer 1

It looks like the three terms on the left are a numerator and the three terms on the right are a denominator. Start by multiplying every single term by x^2.

(x^2 + x - 12) / (x^2 + 2x - 8)

Now rewrite the numerator and denominator by factoring them.

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

Cancel out any factors that appear in both the numerator and denominator to get your final answer.

(x - 3) / (x - 2)

Answer 2

I'm going to assume that you are dividing two fractions, so the problem is to reduce or simplify the following:

[1 + (1/x) - (12/x^2) ]/ [1+ (2/x) - (8/x^2)]

Lets begin by multiplying both the top and bottom by x^2. This gives us:

[x^2 + x - 12]/[x^2 + 2x - 8]

Then we factor the top and bottom

[(x+4)(x-3)]/[(x+4)(x-2)]

And lastly, we divide out the common factor (x+4) to get :

(x-3)/(x-2)

Hope this helps :-)

Answer 3

1 + (1/x) - (12/x^2) / 1+ (2/x) - (8/x^2)
=x^2+x-12/x^2+2x-8
=(x+4(x-3)/(x+4(x-2) =(x-3/(x-2). answer

Answer 4

This isn't as tough as it seems if you just take it in steps. First, rewrite the variables as having negative exponents (not necessary but makes it easier):

1+x^-1-12x^-2/1+2x^-1-8x^-2

Next factor both the numerator and denominator

1+x^-1-12x^-2 = (1+4x^-1)(1-3x^-1)

1+2x^-1-8x^-2 = (1+4x^-1)(1-2x^-1)

since the (1+4x^-1) factor is in both the numerator and the denominator it cancels out leaving (1-3x^-1)/(1-2x^-1).

This is the answer, which can also be written as (1-(3/x))/(1-(2/x))

Answer 5

ahmm.. the problem was confusing...
what do you mean by the symbol ^??