How do you solve f(x)=square root of 2x+1 using the difference quotient? I need to see the steps.

what do you mean by "solve"?

f(x) = √(2x+1)
doesn't involve a difference quotient.

If you want to write down the difference quotient, then that would be

(f(x+h)-f(x))/h
= (√(2(x+h)+1) - √(2x+1))/h
= (√(2x+1+2h) - √(2x+1))/h

Not sure where you want to go with that . . .