I have two solutions for a question about limit
http://tinyurl.com/2pknkb

May I know is (a) correct, or (b)?
What is the reason for the other to be wrong?

Note:
(a) just directly applies l'hopital rule to numerator
(b) is to reduce the numerator using logarithm formula before using l'hopital rule

$$\frac d{dx}(\ln(x+1)-\ln(2)) = \frac d {dx} \ln\left(\frac{x+1} 2\right) = \frac 2 {x+1} \; \frac d {dx}\frac {x+1} 2 = \frac 2 {x+1} \, \frac 1 2 = \frac 1 {x+1}$$