Ta có : $\frac{2}{c}$ = $\frac{1}{a}$ + $\frac{1}{b}$
⇒ $\frac{2}{c}$ = $\frac{a+b}{ab}$
⇔ 2ab = c ( b + a )
⇒ b ( a - c ) - a ( c - b )
= ba - bc - ac + ab
= ( ba + ab ) - bc - ac
= 2ab - bc - ac
= c ( b + a ) - bc - ac
= cb + ca - bc - ac
= ( cb - bc ) + ( ca - ac )
= 0 + 0
= 0
vì b ( a - c ) - a ( c - b ) = 0
⇒ b ( a - c ) = a ( c - b )
⇒ $\frac{a-c}{a}$ = $\frac{c-b}{b}$ ( ĐPCM )