What is the contra-positive of an equality. In order to prove this statement true or false, I need to find the contra-positive of the equation below. I have already tried to prove this by negation which was not successful. $\ \exists \space x \in \Bbb R \space, \exists \space y \in \Bbb R \space| \space \frac{1}{x}+\frac{1}{y}=\frac{1}{x+y} $

Contrapositives are about conditionals ('if .. then' statements), which you don't have here!

There is no such thing as the contrapositive of an identity (equality) or equation.