Question

Answer 1

Sửa đề: Chứng minh \(\frac{5a+3b}{5a-3b}=\frac{5c+3d}{5c-3d}\)

Đặt \(\frac{a}{b}=\frac{c}{d}=k\)

=>a=bk; c=dk

\(\frac{5a+3b}{5a-3b}=\frac{5\cdot bk+3b}{5\cdot bk-3b}=\frac{b\left(5k+3\right)}{b\left(5k-3\right)}=\frac{5k+3}{5k-3}\)

\(\frac{5c+3d}{5c-3d}=\frac{5\cdot dk+3d}{5\cdot dk-3d}=\frac{d\left(5k+3\right)}{d\left(5k-3\right)}=\frac{5k+3}{5k-3}\)

Do đó: \(\frac{5a+3b}{5a-3b}=\frac{5c+3d}{5c-3d}\)