Toán Lớp 7: Chứng minh rằng nếu: a/b=c/d khác 1 thì a+b/a-b=c+d/c-d b,d khác 0

\[\begin{array}{l}
\frac{a}{b} = \frac{c}{d} = k\left( {b;d \ne 0} \right)\\
= > a = kb;c = kd\\
= > \frac{{a + b}}{{a – b}} = \frac{{kb + b}}{{kb – b}} = \frac{{b\left( {k + 1} \right)}}{{b\left( {k – 1} \right)}} = \frac{{k + 1}}{{k – 1}}\\
\frac{{c + d}}{{c – d}} = \frac{{kd + d}}{{kd – d}} = \frac{{d\left( {k + 1} \right)}}{{d\left( {k – 1} \right)}} = \frac{{k + 1}}{{k – 1}}\\
Vay:\frac{{a + b}}{{a – b}} = \frac{{c + d}}{{c – d}}
\end{array}\]