# Please explain this solution to me (with picture)

This is my teacher's work on how to prove a limit statement using delta-epsilon. I understand everything except the where I circled it red. How did he get rid of the term sqrt (x-5) + 2 in the denominator? Where in the world did the zero come from?

• In general, if $a,b,c >0$, we have ${a \over b+c} < {a \over c}$. This follows from $b+c > c$. – copper.hat Oct 18 '14 at 6:15
• can i have an example please? – Elsa Oct 18 '14 at 6:17
• This is just about ordering of numbers. You understand that if the numbers are positive then $b+c > c$, right? – copper.hat Oct 18 '14 at 6:17
• yes i get that part about b + c > c – Elsa Oct 18 '14 at 6:18
• And you understand that if $0 <x < y$ then ${1 \over y} < {1 \over x}$, right? – copper.hat Oct 18 '14 at 6:18