Question

Bài 5. Cho tỉ lệ thưc \(\dfrac{a}{b}=\dfrac{c}{d}\). Hãy chứng minh:

\(\dfrac{4a+3c}{4b+3d}\) = \(\dfrac{4a-3c}{4b-3d}\)

Answer 1

Đặt \(\dfrac{a}{b}=\dfrac{c}{d}=k\)

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

Ta có: \(\dfrac{4a+3c}{4b+3d}=\dfrac{4bk+3dk}{4b+3d}=k\)

\(\dfrac{4a-3c}{4b-3d}=\dfrac{4bk-3dk}{4b-3d}=k\)

Do đó: \(\dfrac{4a+3c}{4b+3d}=\dfrac{4a-3c}{4b-3d}\)