for the function f(x)=3/(2x-1), determine the difference quotient and simplify

Answer 1

f(x+h)-f(x) = 3/(2(x+h)-1) - 3/(2x-1)
= [3(2x-1) - 3(2x+2h-1)]/[(2x-1)(2(x+h)-1)]
= (6x-3-6x-6h+3)/[(2x-1)(2(x+h)-1)]
= -6h/[(2x-1)(2(x+h)-1)]

now divide that by h to get

-6/[(2x-1)(2(x+h)-1)]