Giải thích các bước giải:
Ta có :
$\dfrac{1}{c}=\dfrac{1}{2}.(\dfrac{1}{a}+\dfrac{1}{b})$
$\rightarrow \dfrac{2}{c}=\dfrac{1}{a}+\dfrac{1}{b}$
$\rightarrow \dfrac{1}{c}-\dfrac{1}{a}=\dfrac{1}{b}-\dfrac{1}{c}$
$\rightarrow \dfrac{a-c}{ca}=\dfrac{c-b}{cb}$
$\rightarrow \dfrac{ac}{bc}=\dfrac{a-c}{c-b}$
$\rightarrow \dfrac{a}{b}=\dfrac{a-c}{c-b}$
$\rightarrow đpcm$