Check your derivative of the denominator. It doesn't look right.
limit x-->4 5/ln(x-3) - 5/(x-4)
First, I put the two terms together then derived the top and bottom.
d/dx((5x-20)-5ln(x-3)) / d/dx((x-4)ln(x-3))
5-(5/(x-3)) / 1/(x-3)
Then I derived it a second time and got:
5/(x-3)^2 / -1/(x-3)^2
Which gives me -5. Did I do this correctly? If not, could someone steer me in the right direction? Thank you, I appreciate your help.