# Algebra

O.k. this is similar to the other one I posted. There is a technique in my book how to solve similar ones but the examples aren't so good, so I have no clue were to even start.

1-(1/x)-(12/x^2)
----------------divide top by bottom
1+(6/x)+(9/x^2)

Here are some of my questions.
Do I need to find the LMC and what would that be? Is it x?
I need some guidance on this problem, explanations are welcome.

Here is a good "trick", perhaps it is the one your book is using.

Find the LCM of your denominators and then multiply each term on the top and each term on the bottom by that.
In this case the LCM is x^2, so let's multiply through by that

(x^2 - x - 12)/(x^2 + 6x + 9)

look how easy your expression now looks, on top of that, it factors!!! Yeah!

[(x-4)(x+3)]/[(x+3)(x+3)]
=(x-4)/(x+3), where x is not equal to 3, or else we just divided by zero.

Here is a good "trick", perhaps it is the one your book is using.

Find the LCM of your denominators and then multiply each term on the top and each term on the bottom by that.
In this case the LCM is x^2, so let's multiply through by that

(x^2 - x - 12)/(x^2 + 6x + 9)

look how easy your expression now looks, on top of that, it factors!!! Yeah!

[(x-4)(x+3)]/[(x+3)(x+3)]
=(x-4)/(x+3), where x is not equal to 3, or else we just divided by zero.

My last line should have said:

=(x-4)/(x+3), where x is not equal to -3, or else we just divided by zero.

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