You're trying too hard. Recall that
Thus
Multiply by
which is equal to
Solve the quadratic, I would use the difference of two squares to solve
Edit: Oops, I posted the answer to B not A which is in the quote
From what I can tell you're right (although confusing lol) up to . However, when you took the square root you didn't take the negative.
Taking the reciprocal of both sides:
I got answers of and (or ) as solutions (although only principal solutions because no range is defined in the question)
so discard that solution (from factoring out )