Question

\(\frac{x-2017}{5}-\frac{x-2017}{6}=\frac{x-2017}{7}-\frac{x-2018}{8}\)

Answer 1

\(\frac{x-2017}{5}-\frac{x-2017}{6}=\frac{x-2017}{7}-\frac{x-2017}{8}\)

\(\frac{x-2017}{5}-\frac{x-2017}{6}-\frac{x-2017}{7}+\frac{x-2017}{8}=0\)

\(\left(x-2017\right)\left(\frac{1}{5}-\frac{1}{6}-\frac{1}{7}+\frac{1}{8}\right)=0\)

mà \(\frac{1}{5}-\frac{1}{6}-\frac{1}{7}+\frac{1}{8}\ne0\)

\(\Rightarrow x-2017=0\)

\(\Rightarrow x=2017\)

Vậy x = 2017

Answer 2

\(\Rightarrow\frac{x-2017}{5}-\frac{x-2017}{6}-\frac{x-2017}{7}+\frac{x-2017}{8}=0\)

\(\Rightarrow\left(x-2017\right)\left(\frac{1}{5}-\frac{1}{6}-\frac{1}{7}+\frac{1}{8}\right)=0\)

\(\Rightarrow x-2017=0\)(vì \(\frac{1}{5}-\frac{1}{6}-\frac{1}{7}+\frac{1}{8}\ne0\))

=>x=2017

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