Question

Cho \(\dfrac{a}{b}=\dfrac{c}{d}\) chứng minh 

a) \(\dfrac{ma+nc}{mb+nd}=\dfrac{pa+qc}{pb+qd}\)

b) \(\dfrac{ma+nb}{mc+nd}=\dfrac{pa+qb}{pc+qd}\)

Answer 1

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

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

\(\dfrac{ma+nc}{mb+nd}=\dfrac{mbk+ndk}{mb+nd}=k\)

\(\dfrac{pa+qc}{pb+qd}=\dfrac{pbk+qdk}{pb+qd}=k\)

Do đó: \(\dfrac{ma+nc}{mb+nd}=\dfrac{pa+qc}{pb+qd}\)