How can I simplify this expression without getting confused?

AI Thread Summary
The discussion revolves around simplifying the expression \(\frac{\frac{R}{SC}}{R+\frac{1}{SC}}\). The user struggles with basic math concepts and seeks clarity on the simplification process. They note a difference in notation used by their teacher, specifically regarding the representation of the operation. A key step in the simplification involves multiplying both the numerator and denominator by SC, which the user acknowledges as a helpful insight. The conversation highlights the importance of understanding each step in mathematical simplification.
Femme_physics
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My basic math is failing me again :(


My attempt to simply:
http://imageshack.us/photo/my-images/209/hw2q.jpg/

My teacher's attempt:



Ignore the difference in notation. He writes || which signifies (A x B) / (A + B) = A || B

And yes I'm aware there is more to simplify but I fail to follow him on the first step
 
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I take it R, S and C are three separate variables.
In ##\frac{\frac{R}{SC}}{R+\frac1{SC}}##, multiply top and bottom by SC.
 
Ahh...thank you, I should've seen it!
 
I tried to combine those 2 formulas but it didn't work. I tried using another case where there are 2 red balls and 2 blue balls only so when combining the formula I got ##\frac{(4-1)!}{2!2!}=\frac{3}{2}## which does not make sense. Is there any formula to calculate cyclic permutation of identical objects or I have to do it by listing all the possibilities? Thanks
Since ##px^9+q## is the factor, then ##x^9=\frac{-q}{p}## will be one of the roots. Let ##f(x)=27x^{18}+bx^9+70##, then: $$27\left(\frac{-q}{p}\right)^2+b\left(\frac{-q}{p}\right)+70=0$$ $$b=27 \frac{q}{p}+70 \frac{p}{q}$$ $$b=\frac{27q^2+70p^2}{pq}$$ From this expression, it looks like there is no greatest value of ##b## because increasing the value of ##p## and ##q## will also increase the value of ##b##. How to find the greatest value of ##b##? Thanks
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