Beim Erweitern muss oben und unten mit der gleichen Zahl multipliziert werden.

Hier wird nicht erweitert: ${\displaystyle \frac{1}{3}}\mathrm{\ne }{\displaystyle \frac{1\cdot 2}{3}}={\displaystyle \frac{2}{3}}{\displaystyle \frac{1}{3}}\mathrm{\ne }{\displaystyle \frac{1}{3\cdot 2}}={\displaystyle \frac{1}{6}}{\displaystyle \frac{1}{3}}\mathrm{\ne }{\displaystyle \frac{1\cdot 4}{3\cdot 5}}={\displaystyle \frac{4}{15}}\backslash dfrac\{1\}\{3\}\backslash neq\backslash dfrac\{1\backslash cdot\; 2\}\{3\}=\backslash dfrac\{2\}\{3\}\backslash quad\backslash quad\backslash quad\; \backslash dfrac\{1\}\{3\}\backslash neq\backslash dfrac\{1\}\{3\backslash cdot\; 2\}=\backslash dfrac\{1\}\{6\}\backslash quad\backslash quad\backslash quad\; \backslash dfrac\{1\}\{3\}\backslash neq\backslash dfrac\{1\backslash cdot\; 4\}\{3\backslash cdot\; 5\}=\backslash dfrac\{4\}\{15\}$