Please help to solve lim(x->1) (sqrt(x+a)+b)/(x^2-1)=1
lim(x->1) (sqrt(x+a)+b) / (x^2-1)=1
lim(x->1) (sqrt(x+a)+b) * (sqrt(x+a)-b) / [(x^2-1) * (sqrt(x+a)-b)] = 1
lim(x->1) (x+a-b^2) / [(x-1) * (x+1) * (sqrt(x+a)-b)] = 1
Are you asking for a value of a and b that will make this work?
\(\displaystyle \lim_{x^-\rightarrow1} \frac{\sqrt{x+a}\;+b}{(x^2-1)}=1\)
No idea.