Assuming that the context, rather than the title, is the intended question, there are ambiguities leading to different expressions. For example, "root x plus 2" could mean sqrt(x)+2 or sqrt(x+2). Here's one interpretation:
Start at the end and work backwards:
sqrt(x)/sqrt(x)=1 ("root x over root x"); sqrt(x)/sqrt(x+2) ("root x over root x plus 2"); 1/(sqrt(x)/sqrt(x+2)) ("1 over root x over root x plus 2"); sqrt(x+2)/sqrt(x) (final expression).
The last part could be interpreted: sqrt(x)/(sqrt(x)+2)); 1/(sqrt(x)/(sqrt(x)+2))=(sqrt(x)+2)/sqrt(x)=1+(2/sqrt(x)).