Differentiation using limits

HI there guys, I'm taking calculus for the third time and its been a long time since i can remember my basic algebra and such. So please I ask for patience for this simple work, I understand how to derive this:

lim h->0 f(x+h)-f(x)/h; for example if f(x)=3/2x^2 i know it has to be written as:

lim h->0 3/2(x+h)^2-3/2x^2/h

What i'm having a hard time is including a i binomial and polynomial:

f(x)=2x+3 and f(x)=2x^2+3x-2

All i ask is how to write it, I can figure the answer myself. So far I think its like this:

lim h->0 2(x+3+h)-2x+3/h; however I'm not confident in that answer because all the x variables will be gone and with h=0 the answer be nothing. Please correct me where I am interpreting this wrong.