# manipulating differential operator

#### shreddinglicks

How does the top of part B become the bottom of part B?

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#### skipjack

Forum Staff
It's long division, bearing in mind that further terms can be ignored (as they wouldn't affect the final expression).

#### topsquark

Math Team
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

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#### shreddinglicks

It's long division, bearing in mind that further terms can be ignored (as they wouldn't affect the final expression).
I tried to perform this long division but I am not getting the proper answer. I keep getting a remainder that is my original denominator.