Question

Cho a + 2015 : a - 2015 = b + 2016 : b - 2016            Chứng minh rằng: a : 2015 = b :2016

Answer 1

ta có \(\frac{a+2015}{a-2015}=\frac{b+2016}{b-2016}\)

\(\Rightarrow\frac{\left(a+2015\right)-\left(a-2015\right)}{a-2015}=\frac{\left(b+2016\right)-\left(b-2016\right)}{b-2016}\)

\(\Rightarrow\frac{2015.2}{a-2015}=\frac{2016.2}{b-2016}\)

\(\Rightarrow\frac{2015}{a-2015}=\frac{2016}{b-2016}\)

\(\Rightarrow\frac{a-2015}{2015}=\frac{b-2016}{2016}\)

\(\Rightarrow\frac{a}{2015}-1=\frac{b}{2016}-1\)

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