Evaluate the limit: `lim_{x->4}{8x+4}/{3x-4}` I keep coming up with a limit does not exist?? what am I doing wrong?

Expert Answers
lfryerda eNotes educator| Certified Educator

a limit, we always need to try direct substitution first.  Only if that does not work, do we move on to other methods such as factoring, rationalization, or one-sided limits.  

In this case, direct substitution will get a result for the limit:

`lim_{x->4}{8x+4}/{3x-4}`   replace all x with 4

`={8(4)+4}/{3(4)-4}`   simplify

`={32+4}/{12-4}`

`=36/8`

`=9/2`

The limit evaluates to `9/2` .