Giải thích các bước giải:
\(\begin{array}{l}
\dfrac{{2a + 13b}}{{3a - 7b}} = \dfrac{{2c + 13d}}{{3c - 7d}}\\
\Rightarrow \dfrac{{2a + 13b}}{{2c + 13d}} = \dfrac{{3a - 7b}}{{3c - 7d}}\\
= \dfrac{{14a + 91b}}{{14c + 91d}} = \dfrac{{39a - 91b}}{{39c - 91d}} = \dfrac{{14a + 91b + 39a - 91b}}{{14c + 91d + 39c - 91d}}\\
= \dfrac{{53a}}{{53c}} = \dfrac{a}{c}\\
\dfrac{{2a + 13b}}{{2c + 13d}} = \dfrac{{3a - 7b}}{{3c - 7d}} = \dfrac{{6a + 39b}}{{6c + 39d}} = \dfrac{{6a - 14b}}{{6c - 14d}}\\
= \dfrac{{6a + 39b - 6a + 14b}}{{6c + 39d - 6c + 14d}} = \dfrac{{53b}}{{53d}} = \dfrac{b}{d}\\
\Rightarrow \dfrac{a}{c} = \dfrac{b}{d} \Rightarrow \dfrac{a}{b} = \dfrac{c}{d}
\end{array}\)
