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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?

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

(Sharing a pizza with less folks allows for larger slices)

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