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From Förberedande kurs i matematik 1

Because the denominators are a2−ab=a(a−b) and a−b, both terms will have a common denominator a(a−b) if the top and bottom of the second term are multiplied by a,

a2−b2a+b−2a−b=2a+ba(a−b)−2a−baa=a(a−b)2a+b−2a=ba(a−b).