How Do You Simplify Complex Fractions with Different Denominators?

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To simplify the complex fractions \(\frac{5}{a} + \frac{4}{2a-6} + \frac{-4a}{a^{2}-9}\), the common denominator identified is \(a(a+3)(a-3)\). The user initially struggled with combining the fractions and correctly identifying the common denominator. After some discussion, they clarified that \(2a-6\) can be factored to \(2(a-3)\), and \(a^2-9\) factors to \((a+3)(a-3)\). The conversation highlights the importance of recognizing common factors in the denominators to simplify the expression effectively. Overall, understanding the common denominator is key to combining and simplifying complex fractions.
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Here is the fraction that I don't know how to combine and simplify, please help me out! Thanks! =]

\frac{5}{a} + \frac{4}{2a-6} + \frac {-4a}{a^{2}-9}

I found the common denominator I think: (x+3)(x-3) .. but how do you make {a} in that form?
 
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If I write it as \frac{5}{a}+\frac{2}{(a-3)}-\frac{4a}{(a+3)(a-3)} does it help?
 
Last edited:
Ok, I didn't see the bit you'd edited. The common denominator will be a(a+3)(a-3).
 
oh ok, I knew there wasn't a way to make {a} into {(a+3)(a-3)}. Thanks for your help! =]
 
You're very welcome!
 
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