Use L'Hospital's rule to evaluate to evaluate exactly : Lim x goes to Zero ln(1+3x)-3x/ ln (1-2x)+2x

Show the steps clearly

lim(x→0) [ln(1+3x) - 3x] / [ln(1-2x) + 2x]; this is of the form 0/0
= lim(x→0) [3/(1+3x) - 3] / [-2/(1-2x) + 2], by L'Hopital's Rule
= lim(x→0) [-9x/(1+3x)] / [-4x/(1-2x)]
= (9/4) * lim(x→0) (1-2x)/(1+3x)
= 9/4.

I hope this helps!