# 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?

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Expert Answers

lfryerda | 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` .**