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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? $\displaystyle (1/b)/ (1/b1/a)$ 
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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