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May 22nd, 2015, 04:24 PM  #1 
Member Joined: May 2015 From: U.S.A. Posts: 45 Thanks: 0  How to simplify these two fractions?
$\displaystyle \frac{10}{x3}+\frac{15}{3x}$ I got the common denominator $\displaystyle 4x9$ by multiplying the two denominators together. Then I multiplied the numerators like $\displaystyle 10(3x)$ and $\displaystyle 15(3x)$ so the equation ended up as so: $\displaystyle \frac{3010x+15x45}{4x9}$ and added and subtracted in the numerator to get $\displaystyle \frac{5x15}{4x9}$ And now I'm just puzzled. I can see that three can divide into the numerator and that 9 in the denominator is divisible by 3, too, but that 4 there messes it all up. I might have made a calculation error somewhere, but I must have made the same error three times in a row if that's the case (I kept trying to see if I ended up with easiertoworkwith numbers, so I retried three times), so sorry for any carelessness. The answer is $\displaystyle \frac{5}{x3}$. 
May 22nd, 2015, 04:29 PM  #2 
Math Team Joined: Nov 2014 From: Australia Posts: 689 Thanks: 244 
Firstly, $(x  3)(3  x) \neq 4x  9$. Secondly, it might be easier to note that $3  x = (x  3)$ and find a common denominator that way. 
May 22nd, 2015, 04:44 PM  #3  
Member Joined: May 2015 From: U.S.A. Posts: 45 Thanks: 0  Quote:
Edit: Got $\displaystyle \frac{5}{3x}$, so I got it. Thanks, Azzajazz! I'll be looking more carefully for denominators like this in the future. Last edited by Rexan; May 22nd, 2015 at 04:47 PM.  
May 22nd, 2015, 06:22 PM  #4 
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 14,299 Thanks: 1023  
May 22nd, 2015, 09:01 PM  #5 
Member Joined: May 2015 From: U.S.A. Posts: 45 Thanks: 0  

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