từ \(\frac{a}{b}=\frac{c}{d}\)\(\Rightarrow\)ad = bc \(\Rightarrow\)ad + 2bc = bc + 2ad
\(\Rightarrow\)ab + ad + 2bc + 2cd = ab + 2ad + bc + 2cd
\(\Rightarrow\)a ( b + d ) + 2c ( b + d ) = a ( b + 2d ) + c ( b + 2d )
\(\Rightarrow\)( a + 2c ) ( b + d ) = ( a + c ) ( b + 2d )
\(\frac{a}{b}=\frac{c}{d}\)
\(\Rightarrow\frac{a}{b}=\frac{c}{d}\)\(=\frac{2c}{2d}\)
\(\Rightarrow\frac{a}{b}=\frac{c}{d}=\frac{2c}{2d}=\frac{a+2c}{b+2d}=\frac{a+c}{b+d}\)
\(\Rightarrow\text{(a+2c)(b+d)=(a+c)(b+2d) ( đpcm)}\)
a/b =c/d
a/b=c/d=2c/2d=a+2c/a+2d=a+c/b+d
(a+2c)(b+d)=(b+2d)(a+c)
