# Mistakes give rise to problems- 2

Algebra Level 4

$\dfrac{a+b}{c} = \dfrac{a}{c} + \dfrac{b}{c}$

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

$\dfrac{a}{b+c} = \dfrac{a}{b} + \dfrac{a}{c}$

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

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