Giải thích các bước giải:
sử dụng $\dfrac{a}{b}= \dfrac{c}{d}= \dfrac{a-c}{b-d}= \dfrac{a+c}{b+d}$
a) $\dfrac{a}{b}= \dfrac{c}{d}$
$\Rightarrow \dfrac{5a}{5b}= \dfrac{3c}{3d}$
$\Rightarrow \dfrac{5a-3c}{5b-3d}= \dfrac{5a}{5b}= \dfrac{3c}{3d}= \dfrac{5a+3c}{5b+3d}$
b) $\dfrac{a}{b}= \dfrac{c}{d}\Rightarrow \dfrac{a}{c}= \dfrac{b}{d}$
$\Rightarrow \dfrac{5a}{5c}= \dfrac{3b}{3d}$
$\Rightarrow \dfrac{5a-3b}{5c-3d}= \dfrac{5a}{5c}= \dfrac{3b}{3d}= \dfrac{5a+3b}{5c+3d}$
c) $\dfrac{a}{b}= \dfrac{c}{d}\Rightarrow \dfrac{a}{c}= \dfrac{b}{d}$
$\Rightarrow \dfrac{a}{c}= \dfrac{b}{d}= \dfrac{a+b}{c+d}$
$\Rightarrow \dfrac{a^{3}}{c^{3}}= \dfrac{b^{3}}{d^{3}}= \dfrac{\left ( a+b \right )^{3}}{\left ( c+d \right )^{3}}= \dfrac{a^{3}-b^{3}}{c^{3}-d^{3}}$
