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May 22nd, 2015, 04:41 PM   #1
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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.
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May 22nd, 2015, 05:25 PM   #2
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$\displaystyle \frac{4x + 8}{15} \times \frac{2}{x+2} = \frac{4(\cancel{x + 2})}{15} \times \frac{2}{\cancel{x + 2}} = \frac{8}{15}$
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May 22nd, 2015, 06:19 PM   #3
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Quote:
Originally Posted by skipjack View Post
$\displaystyle \frac{4x + 8}{15} \times \frac{2}{x+2} = \frac{4(\cancel{x + 2})}{15} \times \frac{2}{\cancel{x + 2}} = \frac{8}{15}$
Ah. Thanks for pointing that out. To catch that sort of thing in future problems, I'll just have to be super observant?
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May 22nd, 2015, 08:27 PM   #4
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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.
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May 22nd, 2015, 08:59 PM   #5
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Quote:
Originally Posted by Azzajazz View Post
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.
Okay, that makes a lot sense. Thank you!
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