1. The problem statement, all variables and given/known data Use the ε-δ definition of the limit to prove that lim as x -> 3 of (2x - 6)/(x-3) = 2 2. Relevant equations 3. The attempt at a solution I've started a preliminary analysis for the proof: For any ε>0, find δ=δ(ε) such that 0 < |x - 3| < δ implies that |(2x - 6)/(x-3) - 2|< ε. Simplifying: |(2x - 6)/(x-3) - 2| = |(2x - 6 - 2(x - 3))/(x-3)| = |(2x - 6 - 2x + 6)/(x - 3)| = 0 Where do I go from here? Have I just proven that since the simplified form is 0, which is less than ε, and therefore proven the limit?