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November 22nd, 2017, 03:26 PM   #1
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Question Nested fraction question

Hi,

Can someone explain to me why 1/b doesn't cancel out in this problem?

$\displaystyle (1/b)/
(1/b-1/a)$
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November 22nd, 2017, 03:32 PM   #2
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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 $\dfrac 1 b$
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November 23rd, 2017, 03:37 AM   #3
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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 04:47 AM.
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