\(\dfrac{x-999}{99}+\dfrac{x-896}{101}+\dfrac{x-789}{103}=6\)
\(\Leftrightarrow\dfrac{x-999}{99}-1+\dfrac{x-896}{101}-2+\dfrac{x-789}{103}-3=0\)
\(\Leftrightarrow\dfrac{x-1098}{99}+\dfrac{x-1098}{101}+\dfrac{x-1098}{103}=0\)
\(\Leftrightarrow\left(x-1098\right)\left(\dfrac{1}{99}+\dfrac{1}{101}+\dfrac{1}{103}\right)=0\)
Mà \(\dfrac{1}{99}+\dfrac{1}{101}+\dfrac{1}{103}>0\)
\(\Rightarrow x-1098=0\Leftrightarrow x=1098\)
Vậy x = 1098
\(\dfrac{x-999}{99}+\dfrac{x-896}{101}+\dfrac{x-789}{103}=0\)
⇔\(\dfrac{\left(x-999\right)\cdot10403+\left(x-896\right)10197+\left(x-789\right)\cdot9999}{1029897}=\dfrac{6\cdot1029897}{1029897}\)
⇔\(10403x-10392597+10197x-9136512+9999x-7889211=6179382\)⇔\(10403x+10197x+9999x=6179382+10392597+9136512+7889211\)
⇔\(30599x=33597702\)
⇔\(x=\dfrac{33597702}{30599}\)
⇔\(x=1098\)
Vậy x =1098 là nghiệm của phương trình
