Question

[nhok kon iu]

c/m;

Từ a/b=c/d : 2a+3b/3a-4b = 2c+3d/3c-4d

Answer 1

[Nguyễn Huệ Lam]

Đặt \(\frac{a}{b}=\frac{c}{d}=k\Rightarrow\hept{\begin{cases}a=bk\\c=dk\end{cases}}\)

\(\frac{2a+3b}{3a-4b}=\frac{2bk+3b}{3bk-4b}=\frac{b\left(2k+3\right)}{b\left(3k-4\right)}=\frac{2k+3}{3k-4}\)

\(\frac{2c+3d}{3c-4d}=\frac{2dk+3d}{3dk-4d}=\frac{d\left(2k+3\right)}{d\left(3k-4\right)}=\frac{2k+3}{3k-4}\)

Vậy \(\frac{2a+3b}{3a-4b}=\frac{2c+3d}{3c-4d}\)(đpcm)