# Mistakes give rise to Problems

Algebra Level 4

We know that the denominator can be distributed in a fraction like $\dfrac{a+b}{c} = \dfrac{a}{c} + \dfrac{b}{c}$

But you can't do this in $\dfrac{a}{b+c} = \dfrac{a}{b} + \dfrac{a}{c}$ It will be a mistake if you do it.

But for how many triples $$(a,b,c)$$ of positive integers is the above (second equation) property true?

×