Đặt `\frac{a}{b}` `=` `\frac{c}{d}` `=` `k`
⇒$\left \{ {{a=bk} \atop {c=dk}} \right.$
Mà `\frac{a^2}{b^2}`
⇒ `\frac{a^2}{b^2}` `=` `\frac{(bk)^2}{b^2}` `=` `k^{2}` ( `1` )
⇒ `\frac{2c^2-ac}{2d^2-bd}` `=` `\frac{2(dk)^2-bk.dk}{2.d^2-bd}` `=` `\frac{k^2(2d^2-bd)}{2d^2-bd}` `=` `k^{2}` ( `2` )
Từ ( `1` ) và ( `2` )
⇒`\frac{a^2}{b^2}` `=` `\frac{2c^2-ac}{2d^2-bd}`