it is written as 1 in the numerator then in the denominator it is written as t√1+t this is then subtracted by 1/t lim is t----> 0

How would you factor this?
Would it be by the conjugate?

Look at your first post of this question.

since we cannot extend the √ sign, we have to use brackets to show the end of the square root.
e.g. is it t√(1+t) ???