lim(x->+00) (х+3)*ln((x+1)/(x-2))=...

(x+1)/(x-2)=(x-2+3)/(x-2)=1+3/(x-2)

...=lim(x->+00) (х+3)*ln(1+3/(x-2))=...

домножим и разделим на 3/(x-2)

...=lim(x->+00) (3/(x+2))*(х+3)*ln(1+3/(x-2))/(3/(x-2))=...

используем lim(x->a) (ln(1+f(x)))/f(x)=1 (где f(x)->0 при x->a)

...=lim(x->+00) 3*(х+3)/(x-2)=3 (+0)