a, Đặt \(\frac{a}{b}=\frac{c}{d}=k\Rightarrow a=bk;c=dk\)
Ta có: \(\frac{3a+5b}{2a-7b}=\frac{3bk+5b}{2bk-7b}=\frac{b\left(3k+5\right)}{b\left(2k-7\right)}=\frac{3k+5}{2k-7}\) (1)
\(\frac{3c+5d}{2c-7d}=\frac{3dk+5d}{2dk-7d}=\frac{d\left(3k+5\right)}{d\left(2k-7\right)}=\frac{3k+5}{2k-7}\) (2)
Từ (1) và (2) suy ra đpcm
b,Ta có \(\frac{a}{b}=\frac{c}{d}\Rightarrow\frac{a}{c}=\frac{b}{d}\Rightarrow\frac{a}{c}=\frac{b}{d}=\frac{a+b}{c+d}\Rightarrow\frac{a}{c}\cdot\frac{b}{d}=\frac{a+b}{c+d}\cdot\frac{a+b}{c+d}\Rightarrow\frac{ab}{cd}=\frac{\left(a+b\right)^2}{\left(c+d\right)^2}\) (3)
Lại có \(\frac{ab}{cd}=\frac{a^2}{c^2}=\frac{b^2}{d^2}=\frac{a^2+b^2}{c^2+d^2}\) (4)
Từ (3) và (4) suy ra đpcm
