July 6th, 2017, 04:14 PM  #11  
Member Joined: Jun 2017 From: India Posts: 65 Thanks: 3 
Is this a good definition ? Steps to Find the LCM of Two or More Rational Expressions 1. Factor all denominators completely. 2. The LCM is the product of unique prime factors from the denominators, where each factor is raised to the highest power to which it appears in any denominator. Quote:
1. Factor all denominators completely. 4x = 2.2.x , x2 = x.x , 2x2 =2.x.x So , 2. The LCM is the "product" of unique ( being the only one of its kind; unlike anything else )"pairs of irreducible factors" from the denominators, where each factor is raised to the highest power to which it appears in any denominator. 4x = 2.2.x , x2 = x.x , 2x2 =2.x.x So LCM = 2.2.x.x = 4x2  
July 6th, 2017, 06:20 PM  #12 
Global Moderator Joined: Oct 2008 From: London, Ontario, Canada  The Forest City Posts: 7,729 Thanks: 992 Math Focus: Elementary mathematics and beyond  $\frac{x^24x+4}{x^2+4x12}$ factors as $\frac{(x2)^2}{(x2)(x+6)}$. The numerator's always positive and the denominator is negative for $x\in(6,2)$ and positive everywhere else. So the solution set is $$x\in(\infty,6)\cup(2,\infty)$$ As there's a zero in the denominator at $x=2$, the original function is never equal to zero  though it may appear that way on a plot. Can you guess why? If you have questions about the notation or anything else I'd be happy to answer them. I hope this helped. 
July 6th, 2017, 08:53 PM  #13  
Member Joined: Jun 2017 From: India Posts: 65 Thanks: 3 
Thanks a lot greg1313, I knew it involved factoring, but I didn't know the exact steps though. Quote:
As for the question, Is this an OK definition? Steps to Find the LCM of Two or More Rational Expressions 1. Factor all denominators completely. 2. The LCM is the product of unique prime factors from the denominators, where each factor is raised to the highest power to which it appears in any denominator. 4x = 2.2.x , x2 = x.x , 2x2 =2.x.x So LCM = 2.2.x.x = 4x2 Quote:
Last edited by skipjack; July 10th, 2017 at 03:39 PM.  
July 6th, 2017, 11:17 PM  #14 
Member Joined: Jun 2017 From: India Posts: 65 Thanks: 3 
I like this definition better than the old one , To calculate an LCM for a rational function, follow these steps: 1. Factor all denominator polynomials completely. 2. Make a list that contains one copy of each factor, all multiplied together. 3. The power of each factor in that list should be the highest power that factor is raised to in any denominator. 4. The list of factors and powers you generated is the LCM. 4x = 2.2.x , x2 = x.x , 2x2 =2.x.x So LCM = 2.2.x.x = 4x2 
July 7th, 2017, 02:51 AM  #15 
Senior Member Joined: Apr 2014 From: Glasgow Posts: 2,086 Thanks: 700 Math Focus: Physics, mathematical modelling, numerical and computational solutions 
You calculate the LCM by dividing the product of the two quantities by the greatest common factor (GCF) of the two numbers. Example using 15 and 6: $\displaystyle 15 = 3 \times 5$ $\displaystyle 6 = 2 \times 3$ 3 is in both lists, therefore... $\displaystyle GCF(15, 6) = 3$ $\displaystyle LCM = \frac{Product}{GCF} = \frac{15 \times 6}{3} = \frac{90}{3} = 30$  To get the LCM of more than two quantities, you need to pick any two numbers, calculate the LCM using the above, then repeat the same process with the LCM result. Basically: LCM(15, 6, 9) = LCM(30, 9) = 90  You can do the above methods for variables too; we just assume that variables are like prime numbers and cannot be decomposed further. Last edited by Benit13; July 7th, 2017 at 02:57 AM. 
July 7th, 2017, 08:15 AM  #16 
Member Joined: Jun 2017 From: India Posts: 65 Thanks: 3 
Thanks a lot .

July 7th, 2017, 10:01 AM  #17 
Senior Member Joined: Jun 2015 From: England Posts: 734 Thanks: 207 
Unfortunately I can't see any of the images you post, so I have no idea what your reply to my post#9 was, except that you replied.
Last edited by skipjack; July 7th, 2017 at 05:46 PM. 
July 7th, 2017, 10:06 AM  #18 
Member Joined: Jun 2017 From: India Posts: 65 Thanks: 3 
This PDF has a lot more explanations on how to find the LCM properly Textbook  The Essential Elementary & Intermediate Algebra http://www.jonblakely.com/wpcontent/uploads/5_3.pdf 
July 7th, 2017, 10:09 AM  #19 
Senior Member Joined: Jun 2015 From: England Posts: 734 Thanks: 207 
Yes but I wasn't discussing the LCM particularly. I was addressing your opening post, some of which I don't fully understand. What has x to do with electrons or binary logic etc? 
July 7th, 2017, 10:20 AM  #20 
Member Joined: Jun 2017 From: India Posts: 65 Thanks: 3 
Hello studiot, maybe postimage is blocked in your place. Reposting it with imgur I was just telling that this is the best picture of digital electronics I have come across ... Here, x is electrons x is a quantity x is binary x is a point mass object x is digital logic Last edited by skipjack; July 7th, 2017 at 05:47 PM. 

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