exponent question #2 look over my work!

Question

X to the second power -  4             x + 2

 

_____________________      div    ______

 

            x                                        x-2

 

 

I came up with       1

 

                         _____

 

                            X

 

factor out the x to the second power gives me (X + 2) (x - 2) over X the x-2's cancel out 

 

so I end up X + 2 over X times 1 over X + 2 the X + 2's equal 

 

         1

     ______

 

         x 

 

 

 

                      

Answer 1

Hi Dan-

I'm not sure that I have the starting problem down correctly as it was tough to decipher what you wrote, but was it this:

 

(x² - 4)      x + 2

--------   / --------  

    x           x - 2

 

If this is indeed the original problem, this is how to proceed.  First, treat this like a multiplication problem.  To do that, you must take the inverse of the second part to get:

 

(x² - 4)    x - 2
-------- . --------  
     x       x + 2

 

Now, the next step is to factor (x² - 4):

 

(x - 2)(x + 2)     x - 2
--------------- .  --------
         x             x + 2

 

It is x + 2 that cancels out.  

 

(x - 2)(x + 2)   x - 2
--------------- . --------
         x           x + 2

 

Next, you get:

 

(x - 2)(x - 2)

---------------

        x

 

This simplifies to:

 

(x - 2)²

-------

    x

 

I hope this helps!  Please let me know if you have any other questions.