1 . Đặt $\frac{a}{b}$ = $\frac{c}{d}$ = k
=> a = b.k
=> c = d.k
=>$\frac{a+c}{b+d}$ = $\frac{bk + dk}{b+d}$ = $\frac{k.(b+d)}{b+d}$ = k
=> $\frac{a-c}{b-d}$ = $\frac{bk - dk}{b-d}$ = $\frac{k.(b-d)}{b-d}$ = k
=> $\frac{a}{b}$ = $\frac{bk}{b}$ = k
=>$\frac{a+c}{b+d}$ = $\frac{a-c}{b-d}$ = $\frac{a}{b}$
2. Đặt $\frac{x}{5}$ = $\frac{y}{3}$ = k
=> x = 5k
=> y = 3k
x+y=16
=> 5k + 3k = 16
=>8k= 16
=>k = 2
x = 5k =>x = 10
y = 3k => y = 6