Question - Complex Fraction Simplification
Solution:
\[
\text{Для первого выражения:}
\]
\begin{align*}
& \frac{12}{19} - \left( \frac{1}{12} - \frac{7}{12} + \frac{13}{21} \right) \\
&= \frac{12}{19} - \left( \frac{-6}{12} + \frac{13}{21} \right) \\
&= \frac{12}{19} - \left( -\frac{1}{2} + \frac{13}{21} \right) \\
&= \frac{12}{19} - \left( -\frac{21}{42} + \frac{26}{42} \right) \\
&= \frac{12}{19} - \left( \frac{5}{42} \right) \\
&= \frac{12}{19} - \frac{1}{\frac{42}{5}} \\
&= \frac{12}{19} - \frac{5}{42} \\
&= \frac{42 \cdot 12}{19 \cdot 42} - \frac{19 \cdot 5}{42 \cdot 19} \\
&= \frac{504 - 95}{798} \\
&= \frac{409}{798}.
\end{align*}
\[
\text{Для второго выражения:}
\]
\begin{align*}
& \left( \frac{9}{7} - 25,8 \right) \div \frac{7}{23} \\
&= \left( \frac{9}{7} - \frac{258}{10} \right) \div \frac{7}{23} \\
&= \left( \frac{90}{70} - \frac{1804}{70} \right) \div \frac{7}{23} \\
&= \frac{-1714}{70} \times \frac{23}{7} \\
&= \frac{-245302}{490} \\
&= -500,6173469387755... \approx -500,62.
\end{align*}
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