\(71+65.4=\dfrac{\left(x+140\right)}{x}+260\) \(\left(x\ne0\right)\)
\(\Leftrightarrow71.x+65.4.x=x+140+260.x\)
\(\Leftrightarrow70x=140\Rightarrow x=140:70=2\)
\(71+65.4=\dfrac{\left(x+140\right)}{x}+260\left(x\ne0\right)\Leftrightarrow71+260=\dfrac{\left(x+140\right)}{x}+260\)
\(\Leftrightarrow71=\dfrac{\left(x+140\right)}{x}\)\(\Leftrightarrow71x=x+140\Leftrightarrow70x=140\)
\(\Leftrightarrow x=2\) (thoả mãn đk)
Vậy phương trình có nghiệm duy nhất là x=2