The conclusion is right, but your algebra leaves a lot to be desired. If you mean
(x+1)^(1/2)=(x)^(1/2)*(1+1/x)^(1/2), that's ok. If you mean (x+1)^(1/2)=x^(1/2)+1/(x^(1/2)) or x^(1/2)+(1/x)^(1/2), both of those are wrong. And what happened with the 1/4 power in the denominator? Try to use enough parentheses to make it clear what you mean.