I Why does +bc become negative in the proof of the Euclidian Algorithm?

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The discussion clarifies why +bc becomes negative in the proof of the Euclidean Algorithm, emphasizing that the expression d/(a-qb) is preferred over d/(a+qb). The reasoning is based on the relationship between d/a and d/bc, which leads to d/(a+bc). It is explained that using a-qb simplifies the equation, allowing for a more manageable calculation. The alternative, a+qb, results in larger numbers, making it less useful for subsequent steps. This highlights the importance of choosing the correct form for effective problem-solving in the algorithm.
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In this video, at 5:35 He has d/(a-qb) for the first part. I was not sure how he got that. Why is it not d/(a+qb)?

Because d/a and d/bc implies d/(a+bc)

Why does +bc become negative?
 
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It divides both.

If a=x*d and b=y*d then a-qb=x*d - q*y*d = (x-qy)*d and also a+qb=x*d + q*y*d = (x+qy)*d
The second formula less useful for the next step, however, because it would make numbers larger.
 

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