Question

Tìm x, biết: \(\dfrac{x+2014}{2}+\dfrac{2x+4028}{7}=\dfrac{x+2014}{5}+\dfrac{x+2014}{6}\)

Answer 1

\(\dfrac{x+2014}{2}+\dfrac{2x+4028}{7}=\dfrac{x+2014}{5}+\dfrac{x+2014}{6}\)

\(\Leftrightarrow\dfrac{x+2014}{2}+\dfrac{2.\left(x+2014\right)}{7}-\dfrac{x+2014}{5}-\dfrac{x+2014}{6}=0\)

\(\Leftrightarrow\left(x+2014\right)\left(\dfrac{1}{2}+\dfrac{2}{7}-\dfrac{1}{5}-\dfrac{1}{6}\right)=0\)

\(\Leftrightarrow x+2014=0\Leftrightarrow x=-2014\)