Ta có:
$\dfrac{a}{b} = \dfrac{c}{d}$
Đặt $\dfrac{a}{b} = \dfrac{c}{d} = k$
$\to \begin{cases}a = kb\\c = kd\end{cases}$
Ta được:
$+) \quad \dfrac{a+2012c}{b + 2012d} = \dfrac{kb + 2012.kd}{b + 2012d} = \dfrac{k(b + 2012d)}{b + 2012d} =k$
$+) \quad \dfrac{a- 2013c}{b-2013d}=\dfrac{kb - 2013.kd}{b-2013d} = \dfrac{k(b-2013d)}{b-2013d} = k$
Do đó:
$\dfrac{a+2012c}{b + 2012d} = \dfrac{a- 2013c}{b-2013d}$
