\(\frac{a+2014}{a-2014}=\frac{b+2015}{b-2015}\Rightarrow\left(a+2014\right)\left(b-2015\right)=\left(a-2014\right)\left(b+2015\right)\)
\(\Rightarrow\) \(ab+2014b-2015a-2014.2015=ab+2015a-2014b-2014.2015\)
\(\Rightarrow\) \(\left(ab-ab\right)+\left(-2014.2015+2014.2015\right)=\left(2015a+2015a\right)-\left(2014b+2014b\right)\)
\(\Rightarrow0+0=4030a-4028b\)
\(\Rightarrow4030a=4028b\) \(\Rightarrow\frac{a}{b}=\frac{4028}{4030}=\frac{2014}{2015}\Rightarrow\frac{a}{2014}=\frac{b}{2015}\)
Vậy nếu \(\frac{a+2014}{a-2014}=\frac{b+2015}{b-2015}\) thì \(\frac{a}{2014}=\frac{b}{2015}\) (đpcm)
