No that's wrong.  You can't break up added or subtracted terms
in the numerator and denominator of a fraction the same way as 
you can break up factors in the numerator and denominator of a
fraction.

You can do this either of 2 ways:

1.  By factoring and canceling:



Factor 4 out of top
Factor 2 out of the bottom:



Cancel the 2 into the 4

 




Factor the parenthetical expression in the top as the 
difference of two squares.



Cancel the 's



All that's left is 

And you can multiply that out as

          8x - 10y

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

2.  Yes, it can also be done by long division:



We insert a zero term in xy in the numerator:



                  8x -  10y
8x + 10y)64x² +  0xy - 100y²
         64x² + 80xy 
               -80xy - 100y²  
               -80xy - 100y²

So the answer is the same

          8x - 10y
               
Edwin