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May 23rd, 2019, 05:57 AM  #1 
Member Joined: Oct 2014 From: NJ Posts: 46 Thanks: 2  manipulating differential operator
How does the top of part B become the bottom of part B?

May 23rd, 2019, 12:07 PM  #2 
Global Moderator Joined: Dec 2006 Posts: 20,759 Thanks: 2138 
It's long division, bearing in mind that further terms can be ignored (as they wouldn't affect the final expression).

May 23rd, 2019, 01:59 PM  #3 
Math Team Joined: May 2013 From: The Astral plane Posts: 2,205 Thanks: 901 Math Focus: Wibbly wobbly timeywimey stuff. 
You can also see this as a Maclaurin series in powers of D: $\displaystyle \dfrac{1}{1  \dfrac{D}{3} + \dfrac{4D^2}{9}} \approx 1 + \dfrac{D}{3}  \dfrac{D^2}{3}$ To second order in D. Dan 
May 24th, 2019, 04:53 AM  #4 
Member Joined: Oct 2014 From: NJ Posts: 46 Thanks: 2  

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