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![](https://rs.olm.vn/images/avt/0.png?1311)
Ta có : \(\frac{1}{c}=\frac{1}{2}\left(\frac{1}{a}+\frac{1}{b}\right)\)
\(\Leftrightarrow\frac{1}{c}=\frac{a+b}{2ab}\)
\(\Leftrightarrow ca+cb=2ab\)
\(\Leftrightarrow ac-ab=ab-bc\)
\(\Leftrightarrow a\left(c-b\right)=b\left(a-c\right)\)
\(\Leftrightarrow\frac{a}{b}=\frac{a-c}{c-b}\left(đpcm\right)\)
![](https://rs.olm.vn/images/avt/0.png?1311)
Từ \(\frac{1}{c}=\frac{1}{2}\left(\frac{1}{a}+\frac{1}{b}\right)\)
\(\frac{1}{c}=\frac{1}{2}\left(\frac{b+a}{2ab}\right)\)
\(\frac{1}{c}=\frac{b+a}{2ab}\)
suy ra \(2ab=c\left(b+a\right)\)
\(2ab=cb+ca\)
suy ra \(ab+ab=cb+ca\)
suy a \(ab-cb=ca-ab\)
suy ra \(b\left(a-c\right)=a\left(c-b\right)\)
suy ra \(\frac{a}{b}=\frac{a-c}{c-b}\left(Đpcm\right)\)
![](https://rs.olm.vn/images/avt/0.png?1311)
Từ \(gt\Leftrightarrow\frac{1}{c}=\frac{1}{2}.\frac{a+b}{ab}\)
\(\Leftrightarrow\frac{1}{c}=\frac{a+b}{2ab}\Leftrightarrow c\left(a+b\right)=2ab\Leftrightarrow ac+bc=ab+ab\)
\(\Leftrightarrow ac-ab=ab-bc\Leftrightarrow a\left(c-b\right)=b\left(a-c\right)\)
\(\Rightarrow\frac{a}{b}=\frac{a-c}{b-c}\) (đpcm)
Từ \(gt\Leftrightarrow\frac{1}{c}=\frac{1}{2}.\frac{a+b}{ab}\)
\(\Leftrightarrow\frac{1}{c}=\frac{a+b}{2ab}\Leftrightarrow c\left(a+b\right)=2ab\Leftrightarrow ac+bc=ab+ab\)
\(\Leftrightarrow ac-ab=ab-bc\Leftrightarrow a\left(c-b\right)=b\left(a-c\right)\)
\(\Rightarrow\frac{a}{b}=\frac{a-c}{b-c}\)
\(\Rightarrowđpcm\)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(\frac{1}{c}=\frac{1}{2}\left(\frac{1}{a}+\frac{1}{b}\right)\)
\(\frac{1}{c}=\frac{1}{2}\left(\frac{a+b}{ab}\right)\)
\(2ab=c\left(a+b\right)\)
\(ab+ab=ca+bc\)
\(ab-cb=ac-ab\)
\(b\left(a-c\right)=a\left(c-b\right)\)
\(\Rightarrow\frac{a}{b}=\frac{a-c}{c-b}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(\frac{1}{c}=\frac{1}{2}\left(\frac{1}{a}+\frac{1}{b}\right)\)
\(\Leftrightarrow\frac{1}{c}=\frac{1}{2a}+\frac{1}{2b}\)
\(\Leftrightarrow\frac{1}{c}=\frac{a+b}{2ab}\)
\(\Leftrightarrow2ab=c\left(a+b\right)\)
\(\Leftrightarrow ab+ab=ac+cb\)
\(\Leftrightarrow ab-cb=ac-ab\)
\(\Leftrightarrow b\left(a-c\right)=a\left(c-b\right)\)
\(\Rightarrow\frac{a}{b}=\frac{a-c}{c-b}\) (đpcm)
\(\frac{1}{c}=\frac{1}{2}\left(\frac{1}{a}+\frac{1}{b}\right)\)
\(\frac{2}{c}=\frac{a+b}{ab}\)
\(2ab=ac+ab\)
\(ac-ab=ab-bc\)
\(a\left(c-b\right)=b\left(a-c\right)\)
\(\frac{a}{b}=\frac{a-c}{c-b}\left(đpcm\right)\)