Ý a mình làm 3 cách, ý b tương tự mình làm 1 cách nha.
\(\begin{array}{l}
a)\,\,\frac{{a - b}}{b} = \frac{{c - d}}{d}\\
C1:\,\,\left( {a - b} \right)d = b\left( {c - d} \right)\\
\,\,\,\,\,\,\,\,\,\,ad - bd = bc - bd\\
\,\,\,\,\,\,\,\,\,\,ad = bc\\
\,\,\,\,\,\,\,\,\,\,\frac{a}{b} = \frac{c}{d}\,\,\left( {luon\,\,dung} \right)\\
C2:\,\,\frac{a}{b} = \frac{c}{d} \Rightarrow \frac{a}{b} - 1 = \frac{c}{d} - 1\\
\Rightarrow \frac{{a - b}}{b} = \frac{{c - d}}{d}\\
C3:\,\,\frac{{a - b}}{b} = \frac{{c - d}}{d} \Rightarrow \frac{{a - b}}{b} - \frac{a}{b} = \frac{{c - d}}{d} - \frac{c}{d}\\
\Rightarrow \frac{{a - b - a}}{b} = \frac{{c - d - c}}{d} \Rightarrow \frac{{ - b}}{b} = \frac{{ - d}}{d} = - 1\,\,\left( {luon\,dung} \right)\\
b)\,\,\frac{{a + b}}{a} = \frac{{c + d}}{c}\\
\Leftrightarrow \frac{a}{a} + \frac{b}{a} = \frac{c}{c} + \frac{d}{c} \Leftrightarrow \frac{b}{a} = \frac{d}{c} \Leftrightarrow \frac{a}{b} = \frac{c}{d}\,\,\left( {luon\,\,dung} \right)
\end{array}\)
