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 November 22nd, 2017, 02:26 PM #1 Member   Joined: Mar 2016 From: NJ Posts: 48 Thanks: 2 Nested fraction question Hi, Can someone explain to me why 1/b doesn't cancel out in this problem? $\displaystyle (1/b)/ (1/b-1/a)$
 November 22nd, 2017, 02:32 PM #2 Senior Member     Joined: Sep 2015 From: USA Posts: 2,011 Thanks: 1044 it can $\dfrac{\dfrac 1 b}{\dfrac 1 b - \dfrac 1 a} = \dfrac{1}{1 - \dfrac{\frac 1 a}{\frac 1 b}} = \dfrac{1}{1 - \dfrac b a}$ this is a bit easier to see by multiplying top and bottom by $b$ rather than dividing top and bottom by $\dfrac 1 b$
 November 23rd, 2017, 02:37 AM #3 Math Team   Joined: Jan 2015 From: Alabama Posts: 3,248 Thanks: 887 As to why the "b"s do not cancel, simply put, addition and division do not "play well together". $\displaystyle \frac{b}{a+ b}$ is NOT equal to $\displaystyle \frac{1}{a}$. The only time you can cancel something in numerator and denominator is when you can factor each out- when they are multiplying everything else in the numerator and denominator. Last edited by skipjack; November 23rd, 2017 at 03:47 AM.

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