Prove that:

\(\dfrac{7x-21}{14x-42}=\dfrac{2}{4}\)

Condition determines: \(14x-42\ne0\Leftrightarrow x\ne3\). We have: \(\dfrac{7\left(x-3\right)}{14\left(x-3\right)}=\dfrac{7}{14}=\dfrac{7:7\times2}{14:7\times2}=\dfrac{2}{4}\)

Condition determines: 14x−42≠0⇔x≠3. We have: 7(x−3)14(x−3)=714=7:7×214:7×2=24