Giải:
\(\dfrac{x-2837}{824}+\dfrac{x-2813}{800}+\dfrac{x-1979}{34}+\dfrac{x-1991}{22}=0\)
\(\Leftrightarrow\dfrac{x-2837}{824}+\dfrac{x-2813}{800}+\dfrac{x-1979}{34}+\dfrac{x-1991}{22}+0=0\)
\(\Leftrightarrow\dfrac{x-2837}{824}+\dfrac{x-2813}{800}+\dfrac{x-1979}{34}+\dfrac{x-1991}{22}+2-2=0\)
\(\Leftrightarrow\dfrac{x-2837}{824}+1+\dfrac{x-2813}{800}+1+\dfrac{x-1979}{34}-1+\dfrac{x-1991}{22}-1=0\)
\(\Leftrightarrow\dfrac{x-2837+824}{824}+\dfrac{x-2813+800}{800}+\dfrac{x-1979-34}{34}+\dfrac{x-1991-22}{22}=0\)
\(\Leftrightarrow\dfrac{x-2013}{824}+\dfrac{x-2013}{800}+\dfrac{x-2013}{34}+\dfrac{x-2013}{22}=0\)
\(\Leftrightarrow\left(x-2013\right)\left(\dfrac{1}{824}+\dfrac{1}{800}+\dfrac{1}{34}+\dfrac{1}{22}\right)=0\)
Vì \(\dfrac{1}{824}+\dfrac{1}{800}+\dfrac{1}{34}+\dfrac{1}{22}\ne0\)
Nên \(x-2013=0\)
\(\Leftrightarrow x=2013\)
Vậy \(x=2013\)
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