difference quotient and absolute value

"Evaluate the difference quotient for the given functions. Show all of your work."

The ones I am stuck on are:

a. f(x) = lxl if x<-1 and 0<h<1

b. f(x) = lxl if x>1 and 0<h<1

I know the answers -- a. -1, b. 1 -- but I got them by plugging numbers that fit the parameters into the difference quotient and then evaluating it, which would be fine if I didn't have to show my work. As far as evaluating it directly, thought, I have no idea what to do. (My latex skills are pathetic, so please excuse my not typing all of my work out.)