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.
To solve the given expression:
1. Find the Least Common Multiple (LCM) of the denominators, which are x and x^2. In this case, the LCM is x^2.
2. Multiply each term on the top and each term on the bottom by x^2 to eliminate the fractions. This will result in:
(x^2 - x - 12)/(x^2 + 6x + 9)
3. Simplify the expression by factoring the numerator and the denominator:
Numerator: (x - 4)(x + 3)
Denominator: (x + 3)(x + 3)
4. Cancel out any common factors between the numerator and denominator. In this case, (x + 3) can be canceled out:
(x - 4)/(x + 3)
5. The simplified expression is (x - 4)/(x + 3), with the condition that x is not equal to -3, to avoid dividing by zero.
Note: It's always important to check for any excluded values when simplifying expressions involving fractions. In this case, x cannot be equal to -3 to avoid division by zero.
To solve this problem, you can follow these steps:
1. Find the least common multiple (LCM) of the denominators, which in this case are x and x^2. Since x^2 contains x, the LCM would be x^2.
2. Multiply each term in the numerator and denominator by the LCM (x^2). This step helps to eliminate the denominators and simplify the expression.
Now, let's multiply through by x^2:
(x^2 - x - 12)/(x^2 + 6x + 9)
3. Simplify the expression. In this case, the numerator can be factored: (x-4)(x+3). The denominator is (x+3)(x+3), which can also be written as (x+3)^2.
[(x-4)(x+3)]/[(x+3)(x+3)]
= (x-4)/(x+3)^2
So, the simplified form of the expression is (x-4)/(x+3)^2, where x is not equal to -3 (to avoid division by zero).
Note: It is important to mention any restrictions like x≠-3, as dividing by zero is undefined.