\(x:2=x:3\)
\(\Leftrightarrow\left(x:2\right)-\left(x:3\right)=0\)
\(\Leftrightarrow\left(x.\frac{1}{2}\right)-\left(x.\frac{1}{3}\right)=0\)
\(\Leftrightarrow x.\left(\frac{1}{2}-\frac{1}{3}\right)=0\)
\(\Leftrightarrow x.\frac{1}{6}=0\)
\(\Leftrightarrow x=0\)