March 6th, 2017, 09:59 AM  #11  
Newbie Joined: Feb 2017 From: USA Posts: 28 Thanks: 1  Quote:
For my understanding  is the numerator $\displaystyle 2u^21$ considered a term in its entirety or can one 'pull out' the variable? I seem to remember (perhaps incorrectly) that you can reduce variables across the division sign by subtracting the powers. Is there a reference that I can review for this rule? Can someone name the rule or where to find it? Thanks again!  
March 6th, 2017, 10:00 AM  #12 
Newbie Joined: Feb 2017 From: USA Posts: 28 Thanks: 1  
March 6th, 2017, 10:29 AM  #13  
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 11,824 Thanks: 760  Quote:
1: look up "law of exponents" 2: google "simplifying algebraic fractions" 3: get a girlfriend who's a math expert  
March 6th, 2017, 11:15 AM  #14  
Math Team Joined: Jul 2011 From: North America, 42nd parallel Posts: 3,372 Thanks: 233  Quote:
 
March 6th, 2017, 11:30 AM  #15 
Global Moderator Joined: Dec 2006 Posts: 18,691 Thanks: 1523 
Although there are some videos and other study materials available on the internet, it would be a big advantage to use an elementary algebra textbook. It could be an old textbook that's out of copyright and available on the internet or a physical book. It won't matter if it's a bit dated, as the relevant terminology hasn't changed much. One can learn algebra over a period of six years or more at school, so don't expect to cover it all in just a week.

March 6th, 2017, 11:41 AM  #16  
Senior Member Joined: May 2016 From: USA Posts: 917 Thanks: 368  Quote:
 
March 6th, 2017, 12:16 PM  #17  
Newbie Joined: Feb 2017 From: USA Posts: 28 Thanks: 1  Quote:
I mention precalc. because it is my understanding that most of those texts cover some basic algebra before advancing. One week, no... two months, eh... maybe! I really am looking to ferret out the key concepts that I may have forgotten or mislearned. Thanks again for your advice!  
March 6th, 2017, 12:23 PM  #18  
Newbie Joined: Feb 2017 From: USA Posts: 28 Thanks: 1  Quote:
Thanks in advance.  
March 6th, 2017, 01:39 PM  #19 
Math Team Joined: Jul 2011 From: Texas Posts: 2,722 Thanks: 1375 
$\dfrac{\sqrt{4x^2}\frac{1}{2\sqrt{4x^2}}}{4x^2} \cdot \dfrac{2\sqrt{4x^2}}{2\sqrt{4x^2}}$ $\dfrac{2(4x^2)  1}{2(4x^2)^{3/2}}$ $\dfrac{72x^2}{2(4x^2)^{3/2}}$ 
March 6th, 2017, 01:42 PM  #20  
Senior Member Joined: May 2016 From: USA Posts: 917 Thanks: 368  Quote:
Remember that an expression inside parentheses merely represents a single number. You can view the expression as a single term. $\dfrac{ac + ad}{ab} = \dfrac{\cancel a(c + d)}{\cancel ab} = \dfrac{c + d}{b}.$ $a,\ b,\ c,\ d \ne 0\ and\ a \ne 1 \implies$ $\dfrac{c + d}{b} = \dfrac{a(c + d)}{ab} = \dfrac{ac + ad}{ab} \ne \dfrac{ac + d}{ab}.$ The problem with "precalc" is that there does not seem to be a standard definition for it. In some schools, it is college algebra. In others it is an introduction to analysis and applications of calculus. Because you previously studied algebra, I'd start with a high school algebra text. It may be that with a bit of practice, it all comes back to you. If, however, it is a struggle, you are not ready for calculus. If you breeze through a high school algebra text getting almost 100% of the problems with answers right, get a college algebra text. In college, they generally cover all the algebra (except maybe for trig functions) you will need for calculus in a single year. See if you get that easily. If not, take a college algebra course before you tackle calculus.  

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