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May 22nd, 2015, 04:41 PM  #1 
Member Joined: May 2015 From: U.S.A. Posts: 45 Thanks: 0  Dividing two fractions with equations in the numerators
$\displaystyle \frac{4x+8}{15} \div \frac{3x+6}{6}$ I changed the equation by turning it into multiplication and changing the second fraction to its reciprocal: $\displaystyle \frac{4x+8}{15} \times \frac{6}{3x+6}$ I divided the second fraction by $\displaystyle \frac {3}{3}$: $\displaystyle \frac{4x+8}{15} \times \frac{2}{x+2}$ but multiplying those together just confused me more, because I got a numerator divisible by 4 and a denominator divisible by 15, but, as far as I can see, I can't do anything with either of them: $\displaystyle \frac{8x+16}{15x+30}$ So I'm stuck. The answer is $\displaystyle \frac{8}{15}$, and I don't see how to get rid of the x's or the 16 and 30. Let me know if you find anything strange; I might have made a typo. 
May 22nd, 2015, 05:25 PM  #2 
Global Moderator Joined: Dec 2006 Posts: 20,467 Thanks: 2038 
$\displaystyle \frac{4x + 8}{15} \times \frac{2}{x+2} = \frac{4(\cancel{x + 2})}{15} \times \frac{2}{\cancel{x + 2}} = \frac{8}{15}$

May 22nd, 2015, 06:19 PM  #3 
Member Joined: May 2015 From: U.S.A. Posts: 45 Thanks: 0  
May 22nd, 2015, 08:27 PM  #4 
Math Team Joined: Nov 2014 From: Australia Posts: 689 Thanks: 244 
It's usually a good idea to factor the numerator and denominator of your fraction. That will make it clear as to whether there are any common factors.

May 22nd, 2015, 08:59 PM  #5 
Member Joined: May 2015 From: U.S.A. Posts: 45 Thanks: 0  

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dividing, equations, fractions, numerators 
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