OK, so what about this one?

f( x ) = ( 3x^3 + 2 ) / ( x^2 - x - 7 )

If we look at 3x^3 / x^2 , we find that the x^2 WILL divide in... 
But, there's going to be some x stuff left over to deal with.  This is when you need to start in with some long division...  and we get to ignore the remainder!

 

 

 

 

 

 

( x^2 - x - 7 ) / ( 3x^3 + 0x^2 + 0x + 2 )  ...  which gives 3x^3 - 3x^2 - 21x  ...  subtracting gives 3x^2 + yadda  ...  The 3x + 3 is the slant asymptote.  It's the line y = 3x + 3

You can stop here since the rest will be remainder stuff.
 

a graph with the slant asymptote y = 3x + 3

 


TRY IT:

Find the slant asymptote of

f( x ) = ( 5x^2 - 3x + 1 ) / ( x + 2 )