Answer :
[tex]3x=4y=12z \Rightarrow x=4z,y=3z
\\ \frac{xy}{x+y}
\\
\\ \frac{4z3z}{4z+3z}
\\
\\ \frac{12z^2}{7z}
\\
\\ \frac{12}{7} z[/tex]
So, I proved that [tex]\frac{xy}{x+y} \ne z[/tex]
So, I proved that [tex]\frac{xy}{x+y} \ne z[/tex]