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x-2 / x^2 + 4x -12

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2 Answers

I took this problem to be x-2/(x^2+4x-12). I do not think it is an addition problem. In this form it is a lot easier.
 
The first step would be to change the denominator(I was taught it as a reverse FOIL). You can simplify the denominator to (x+6)(x-2). Therefore, you now have (x-2)/(x+6)(x-2).
 
As you can see, you have an (x-2) in the numerator and the denominator so you can cancel these out. This leaves you 1/(x+6).
Step 1.
We need to get a common denominator because it is a addition problem. So we will still be using the basic rules of addition in fractions. And whatever you do to the bottom you must do to the top, also whatever you do to oneside you must do to the other 
 
 (x-2)/x^2 +( 4x-12)/1=
 
(x^2)(x-2)/x^2+(4x-12)(x^2)/1(x^2)=
 
Step 2.
 
Remember the rule of exponents because when we multiple x^2 * (x-2) we know that the x^2*x is x^3 because we add the exponents while also multiplying the (x) which becomes...
 
(x^3-2)/x^2+(4x^3-12x^2)/x^2
 
 
Step 3 
 
Now that we have the same denominator and we also have a balanced equation we can combine the top part of the fraction to make one fraction and begin to simplify the equation.
 
(x^3-2x^2)+(4x^3-12x^2)/x^2=
 
5x^3-14x^2/x^2=
 

Notes when adding exponets such as x^3 and 4x^3 it is not 4x^6 or 5x^6. Refer to your book about why.

 

Step 4

 

The end of the the equation is to make sure that it is simplified to the basic equations. One way to do this is to find out what are the commonalities of the equation. In this instance the commonalities is x^2 which can be deduced from the equation as followed. 

 

x^2(5x-14)/x^2 =

Note: The x^2 cancels each other becoming the invisible 1 in front of the answer. 

Answer:

 invisible>>>>  1   (5x-14)

 

 

 
 
 
 
 
 
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