cho a/b = c/d . CM : a) a/a-b = c/c-d b/) a/b =a+c/b+d c)a/3a+b = c/3c+d

Đáp án:

$\begin{array}{l}
\dfrac{a}{b} = \dfrac{c}{d} = k \Rightarrow \left\{ \begin{array}{l}
a = b.k\\
c = d.k
\end{array} \right.\\
a)\dfrac{a}{{a – b}} = \dfrac{{b.k}}{{b.k – b}} = \dfrac{{b.k}}{{b.\left( {k – 1} \right)}} = \dfrac{k}{{k – 1}}\\
\dfrac{c}{{c – d}} = \dfrac{{d.k}}{{dk – d}} = \dfrac{{dk}}{{d.\left( {k – 1} \right)}} = \dfrac{k}{{k – 1}}\\
 \Rightarrow \dfrac{a}{{a – b}} = \dfrac{c}{{c – d}}\\
b)\\
\dfrac{{a + c}}{{b + d}} = \dfrac{{b.k + d.k}}{{b + d}} = \dfrac{{k.\left( {b + d} \right)}}{{b + d}} = k\\
 \Rightarrow \dfrac{a}{b} = \dfrac{{a + c}}{{b + d}} = k\\
c)\\
\dfrac{a}{{3a + b}} = \dfrac{{b.k}}{{3bk + b}} = \dfrac{k}{{3k + 1}}\\
\dfrac{c}{{3c + d}} = \dfrac{{dk}}{{3dk + d}} = \dfrac{k}{{3k + 1}}\\
 \Rightarrow \dfrac{a}{{3a + b}} = \dfrac{c}{{3c + d}}
\end{array}$