Question

CM rằng nếu: a/ b=c/ d thì a+b/ a−b= c+d/ c−d
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Answer 1

Ta có: \(\frac{a}{b}=\frac{c}{d}\Leftrightarrow\frac{a}{c}=\frac{b}{d}=\frac{a+b}{c+d}=\frac{a-b}{c-d}\)

\(\Leftrightarrow\frac{a+b}{c+d}=\frac{a-b}{c-d}\Leftrightarrow\frac{a+b}{a-b}=\frac{c+d}{c-d}\)( đpcm )

Answer 2

Đặt \(\frac{a}{b}=\frac{c}{d}=k\Rightarrow a=bk;c=dk\)

\(\frac{a+b}{a-b}=\frac{c+d}{c-d}\Rightarrow\frac{a+b}{c+d}=\frac{a-b}{c-d}\)

\(\frac{a+b}{c+d}=\frac{bk+b}{dk+d}=\frac{b.\left(k+1\right)}{d.\left(k+1\right)}=\frac{b}{d}\left(1\right)\)

\(\frac{a-b}{c-d}=\frac{bk-b}{dk-d}=\frac{b.\left(k-1\right)}{d.\left(k+1\right)}=\frac{b}{d}\left(2\right)\)

Từ ( 1 ) và ( 2 ) => \(\frac{a+b}{c+d}=\frac{a-b}{c-d}\)hay \(\frac{a+b}{a-b}=\frac{c+d}{c-d}\)( đpcm )