TeX Quellcode:

\begin{array}{rcl} \genfrac{}{}{1pt}{0}{\frac{a}{b}-\frac{b}{a}}{\frac{1}{b}+\frac{1}{a}} \; : \; \left(a-b\right) &=& \genfrac{}{}{1pt}{0}{\frac{a^2}{ab}-\frac{b^2}{ab}}{\frac{a}{ab}+\frac{b}{ab}} \; : \; \left(a-b\right) \cr\cr &=& \genfrac{}{}{1pt}{0}{\frac{a^2-b^2}{ab}}{\frac{a+b}{ab}} \; : \; \left(a-b\right) \cr\cr &=& \dfrac{a^2-b^2}{ab} \; : \; \dfrac{a+b}{ab} \; : \; \left(a-b\right) \cr\cr &=& \dfrac{a^2-b^2}{ab} \; \cdot \; \dfrac{ab}{a+b}\cdot \dfrac{1}{a-b} \cr\cr &=& \dfrac{a^2-b^2}{1} \; \cdot \; \dfrac{1}{a+b}\cdot \dfrac{1}{a-b} \cr\cr&=& \dfrac{a^2-b^2}{(a+b) \cdot (a-b)} \cr\cr&=& \dfrac{(a+b)(a-b)}{(a+b)(a-b)} \cr\cr&=& 1\end{array}