Toán Lớp 7: a). Cho a/b=c/d( với b+d khác 0)
CM: a/b=a+c/b+c
b). Cho a/b+c/d( a,b,c,d khác 0)
CM: a-b/a=c-d/c
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Toán Lớp 7: a). Cho a/b=c/d( với b+d khác 0)
CM: a/b=a+c/b+c
b). Cho a/b+c/d( a,b,c,d khác 0)
CM: a-b/a=c-d/c
Comments ( 1 )
Giải đáp:
$\begin{array}{l}
a)\dfrac{a}{b} = \dfrac{c}{d} = k\\
\Leftrightarrow \left\{ \begin{array}{l}
a = b.k\\
c = d.k
\end{array} \right.\\
\Leftrightarrow \dfrac{{a + c}}{{b + d}} = \dfrac{{b.k + d.k}}{{b + d}} = \dfrac{{\left( {b + d} \right).k}}{{b + d}} = k\\
\Leftrightarrow \dfrac{a}{b} = \dfrac{{a + c}}{{b + d}}\left( { = k} \right)\\
Vay\,\dfrac{a}{b} = \dfrac{{a + c}}{{b + d}}\\
b)\dfrac{a}{b} = \dfrac{c}{d} = k \Leftrightarrow \left\{ \begin{array}{l}
a = b.k\\
c = d.k
\end{array} \right.\\
\dfrac{{a – b}}{a} = \dfrac{{b.k – b}}{{b.k}} = \dfrac{{\left( {k – 1} \right).b}}{{b.k}} = \dfrac{{k – 1}}{k}\\
\dfrac{{c – d}}{c} = \dfrac{{d.k – d}}{{d.k}} = \dfrac{{\left( {k – 1} \right).d}}{{d.k}} = \dfrac{{k – 1}}{k}\\
\Leftrightarrow \dfrac{{a – b}}{a} = \dfrac{{c – d}}{c}
\end{array}$