Mistakes give rise to problems- 2

Algebra Level 4

a+bc=ac+bc\dfrac{a+b}{c} = \dfrac{a}{c} + \dfrac{b}{c}

We know that we can split a fraction like what we did above, but you can't do this in

ab+c=ab+ac\dfrac{a}{b+c} = \dfrac{a}{b} + \dfrac{a}{c}

This is a false property, it will be a mistake if you do it! However, it holds for certain values of integers a,b,a,b, and c.c. If a,b,c10a,b,c \leq 10 and a,b,ca,b,c are non-negative integers, then for how many ordered triples (a,b,c)(a,b,c) is ab+c=ab+ac \frac a{b+c} = \frac ab + \frac ac seen to be true?


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