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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? $\displaystyle \frac{10}{x-3}+\frac{15}{3-x}$ I got the common denominator $\displaystyle 4x-9$ by multiplying the two denominators together. Then I multiplied the numerators like $\displaystyle 10(3-x)$ and $\displaystyle 15(3-x)$ so the equation ended up as so: $\displaystyle \frac{30-10x+15x-45}{4x-9}$ and added and subtracted in the numerator to get $\displaystyle \frac{5x-15}{4x-9}$ 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 easier-to-work-with numbers, so I retried three times), so sorry for any carelessness. The answer is $\displaystyle \frac{-5}{x-3}$. 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. Thanks from Rexan May 22nd, 2015, 04:44 PM   #3
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 Originally Posted by Azzajazz 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.
Oh jeez. I multiplied the x and -x to get -2x. I thought it looked strange. My bad. I'll try again, and thanks for pointing that out about -(x - 3).

Edit: Got $\displaystyle \frac{5}{3-x}$, 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
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Quote:
 Originally Posted by Rexan $\displaystyle \frac{10}{x-3}+\frac{15}{3-x}$
You can rewrite this way: 10 / (x-3) - 15 / (x-3)
so: -5 / (x-3)
And that can be rewritten: 5 / (3-x) May 22nd, 2015, 09:01 PM   #5
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 Originally Posted by Denis You can rewrite this way: 10 / (x-3) - 15 / (x-3) so: -5 / (x-3) And that can be rewritten: 5 / (3-x)
Wow, looks like you were able to snap that answer up pretty quick. Thanks for posting! Tags fractions, simplify Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post linhbui Elementary Math 1 November 11th, 2013 08:04 PM watkd Algebra 2 January 10th, 2012 10:10 AM Valar30 Algebra 4 June 11th, 2011 09:56 PM Openuser Elementary Math 1 October 27th, 2010 10:40 AM nova3421 Algebra 1 September 9th, 2009 10:03 AM

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