Question

cho a/b = c/d cm (a+3c)(b-d) =(a-c)(b+3d)

Answer 1

Đặt :

\(\dfrac{a}{b}=\dfrac{c}{d}=k\)

\(\Leftrightarrow\left\{{}\begin{matrix}a=bk\\c=dk\end{matrix}\right.\)\(\left(k\ne0\right)\)

Ta có :

\(\left(a+3c\right)\left(b-d\right)=\left(bk+3dk\right)\left(b-d\right)=k\left(b+3d\right)\left(b-d\right)\left(1\right)\)

\(\left(a-c\right)\left(b+3d\right)=\left(bk-dk\right)\left(b+3d\right)=k\left(b-d\right)\left(b+3d\right)=k\left(b+3d\right)\left(b-d\right)\left(2\right)\)

Từ \(\left(1\right)+\left(2\right)\Leftrightarrowđpcm\)