Đặt a$\frac{a}{b}$ = a$\frac{c}{d}$ = k
thì a = bk ; c = dk
- Vì ( a + 2c )( b + d ) = ( a + c )( b + 2d )
⇒ $\frac{a + 2c}{a + c}$ = $\frac{b + 2d}{b + d}$
Ta có :
VT = $\frac{a + 2c}{a + c}$ = $\frac{bk + 2dk}{bk + dk}$
= $\frac{k( b + 2d )}{k( b + d )}$
= $\frac{b + 2d}{b + d}$
= VP
Vậy ( a+2c )( b+d ) = ( a+c )( b+2d ) (đpcm)