Cho a/b = c/d. Chứng minh a / (a - b) = c / (c - d)
Cho \(\frac{a}{b} = \frac{c}{d}\). Chứng minh: \(\frac{a}{{a - b}} = \frac{c}{{c - d}}\).
\(\frac{a}{b} = \frac{c}{d}\)
⇔ \(\frac{b}{a} = \frac{d}{c}\)
⇔ \(\frac{b}{a} = \frac{d}{c}\)
⇔ \(1 - \frac{b}{a} = 1 - \frac{d}{c}\)
⇔ \(\frac{{a - b}}{a} = \frac{{c - d}}{c}\)
⇔ \(\frac{a}{{a - b}} = \frac{c}{{c - d}}\).