Các bước giải:
\(\begin{array}{l}
1)\,\dfrac{a}{b} = \dfrac{c}{d} = \dfrac{{a - c}}{{b - d}} = \dfrac{{a + c}}{{b + d}}\\
\Rightarrow \dfrac{{a - c}}{{a + c}} = \dfrac{{b - d}}{{b + d}}\\
2)\dfrac{a}{b} = \dfrac{c}{d} \Rightarrow \dfrac{{{a^{2020}}}}{{{b^{2020}}}} = \dfrac{{{c^{2020}}}}{{{d^{2020}}}}\\
\Rightarrow \dfrac{{{a^{2020}} - {b^{2020}}}}{{{b^{2020}}}} = \dfrac{{{c^{2020}} - {d^{2020}}}}{{{d^{2020}}}}\\
\Rightarrow \dfrac{{{a^{2020}} - {b^{2020}}}}{{{c^{2020}} - {d^{2020}}}} = \dfrac{{{b^{2020}}}}{{{d^{2020}}}}\\
Lai\,co:\dfrac{{{a^{2020}}}}{{{b^{2020}}}} = \dfrac{{{c^{2020}}}}{{{d^{2020}}}}\\
\Rightarrow \dfrac{{{a^{2020}} + {b^{2020}}}}{{{c^{2020}} + {d^{2020}}}} = \dfrac{{{b^{2020}}}}{{{d^{2020}}}}\\
\Rightarrow \dfrac{{{a^{2020}} - {b^{2020}}}}{{{c^{2020}} - {d^{2020}}}} = \dfrac{{{a^{2020}} + {b^{2020}}}}{{{c^{2020}} + {d^{2020}}}}\\
\Rightarrow \dfrac{{{a^{2020}} - {b^{2020}}}}{{{a^{2020}} + {b^{2020}}}} = \dfrac{{{c^{2020}} - {d^{2020}}}}{{{c^{2020}} + {d^{2020}}}}
\end{array}\)
