## Give an epsilon, delta verification that lim_{x to 1} (x^3+x)/(3x-2) =2.

I'm new to this site (like 10 minutes new) and I read that I have to post each question individually. I have like 2 more after this question on my review sheet that I'm struggling with. (would have help if the prof gave an answer sheet!) Well, here it goes. Thanks in advance.

Give an epsilon, delta verification that lim_{x to 1} (x^3+x)/(3x-2) =2.

I know that I have to state: Let e>0. Find delta>0 s.t. if x satisfies 0<(this is where im stuck)<delta then |f(x)-2|<e.

Also, I've attempted to simplify such as:

f(x)-2=(x^3+x)/(3x-2)-2=(x^3-5x+4)/(3x-2) I'm getting stuck at simplifying this i don't know why or am I to just leave it as is and go on with my proof? ugh confused.