Question

\(\dfrac{x-7}{2010}\)+\(\dfrac{x-604}{471}\)+\(\dfrac{x-2}{403}\)=9

 

Answer 1

\(\dfrac{x-7}{2010}+\dfrac{x-604}{471}+\dfrac{x-2}{403}=9\)

\(\Leftrightarrow\dfrac{x-7}{2010}-1+\dfrac{x-604}{417}-3+\dfrac{x-2}{403}-5=0\)

\(\Leftrightarrow\dfrac{x-2017}{2010}+\dfrac{x-2017}{471}+\dfrac{x-2017}{403}=0\)

\(\Leftrightarrow\left(x-2017\right)\left(\dfrac{1}{2010}+\dfrac{1}{471}+\dfrac{1}{403}\right)=0\)

Mà \(\dfrac{1}{2010}+\dfrac{1}{471}+\dfrac{1}{403}\ne0\)

\(\Rightarrow x-2017=0\Leftrightarrow x=2017\)