Cho 1/c=1/2(1/a+1/b) (với a, b, c ≠ 0, b ≠ c). Chứng minh rằng: a/b=(a-c)/c-d) .

$\frac{1}{c}=\frac{1}{2}(\frac{1}{a}+\frac{1}{b})$ (với a, b, c ≠ 0, b ≠ c)

$\iff \frac{1}{c}=\frac{a+b}{2ab}$

$\iff$ 2ab = a(a + b)

$\iff$ 2ab = ac + bc

$\iff$ ab + ab = ac + bc

$\iff$ ab – bc = ac – ab

$\iff$ b(a – c) = a(c – b)

$\iff \frac{a}{b}=\frac{a-c}{c-b}$

Vậy $\frac{a}{b}=\frac{a-c}{c-b}$.