Giải thích các bước giải:
\(\begin{array}{l}
4,\\
\dfrac{a}{b} = \dfrac{c}{d}\\
\Leftrightarrow ad = bc\\
\Leftrightarrow - ad = - bc\\
\Leftrightarrow ab + \left( { - ad} \right) = ab + \left( { - bc} \right)\\
\Leftrightarrow ab - ad = ab - bc\\
\Leftrightarrow a.\left( {b - d} \right) = b.\left( {a - c} \right)\\
\Leftrightarrow \dfrac{a}{{a - c}} = \dfrac{b}{{b - d}}\\
6,\\
\dfrac{a}{b} = \dfrac{c}{d}\\
\Leftrightarrow ad = bc\\
\Leftrightarrow ad - cd = bc - cd\\
\Leftrightarrow d\left( {a - c} \right) = c.\left( {b - d} \right)\\
\Leftrightarrow \dfrac{d}{{b - d}} = \dfrac{c}{{a - c}}\\
\Rightarrow \dfrac{c}{{a - c}} = \dfrac{d}{{b - d}}\\
8,\\
\dfrac{a}{b} = \dfrac{c}{d}\\
\Leftrightarrow ad = bc\\
\Leftrightarrow - ad = - bc\\
\Leftrightarrow ab + \left( { - ad} \right) = ab + \left( { - bc} \right)\\
\Leftrightarrow ab - ad = ab - bc\\
\Leftrightarrow a.\left( {b - d} \right) = b.\left( {a - c} \right)\\
\Leftrightarrow \dfrac{{b - d}}{b} = \dfrac{{a - c}}{a}\\
\Rightarrow \dfrac{{a - c}}{a} = \dfrac{{b - d}}{b}\\
15,\\
\dfrac{a}{b} = \dfrac{c}{d}\\
\Leftrightarrow ad = bc\\
\Leftrightarrow - ad = - bc\\
\Leftrightarrow ac + \left( { - ad} \right) = ac + \left( { - bc} \right)\\
\Leftrightarrow ac - ad = ac - bc\\
\Leftrightarrow a\left( {c - d} \right) = c.\left( {a - b} \right)\\
\Leftrightarrow \dfrac{a}{{a - b}} = \dfrac{c}{{c - d}}\\
17,\\
\dfrac{a}{b} = \dfrac{c}{d}\\
\Leftrightarrow ad = bc\\
\Leftrightarrow ad - bd = bc - bd\\
\Leftrightarrow d.\left( {a - b} \right) = b.\left( {c - d} \right)\\
\Leftrightarrow \dfrac{{a - b}}{b} = \dfrac{{c - d}}{d}
\end{array}\)
