Reducing Fractions - (bc-ab) / (a^3 - ac^2 - 2ab^2 + 2b^2c)

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The discussion focuses on reducing the fraction (bc-ab) / (a^3 - ac^2 - 2ab^2 + 2b^2c). The user is trying to simplify it to have only a (b) in the numerator. They propose a transformation but struggle with factoring the denominator due to the presence of (a^2 - c^2). Another participant points out that (a^2 - c^2) can be factored as (a-c)(a+c), allowing for simplification. This exchange highlights the importance of recognizing factoring opportunities in algebraic expressions.
lokisapocalypse
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Hey guys,

I'm working on this project for my research and I am having trouble reducing a fraction. The fraction is:

(bc-ab) / (a^3 - ac^2 - 2ab^2 + 2b^2c)

I am almost positive that I can end up with only a (b) on top but I am not sure how. I had an idea:

(b(c-a)) / (a(a^2-c^2) - 2b^2(a - c))

I want to factor out a (a - c) on the bottom but can't because I have (a^2 - c^2).
 
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lokisapocalypse said:
Hey guys,

I'm working on this project for my research and I am having trouble reducing a fraction. The fraction is:

(bc-ab) / (a^3 - ac^2 - 2ab^2 + 2b^2c)

I am almost positive that I can end up with only a (b) on top but I am not sure how. I had an idea:

(b(c-a)) / (a(a^2-c^2) - 2b^2(a - c))

I want to factor out a (a - c) on the bottom but can't because I have (a^2 - c^2).

a^2-c^2= (a-c)(a+c), so you can factor out (a-c) from the denominator.
 
Thanks, its been a long time since simple stuff like this. You forget about it real quick.
 
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