\(\dfrac{4-x}{96}+1+\dfrac{3-x}{97}+1=\dfrac{2-x}{98}+1+\dfrac{1-x}{99}+1\)
\(\Leftrightarrow\dfrac{100-x}{96}+\dfrac{100-x}{97}-\dfrac{100-x}{98}-\dfrac{100-x}{99}=0\)
\(\Leftrightarrow\left(100-x\right)\left(\dfrac{1}{96}+\dfrac{1}{97}-\dfrac{1}{98}-\dfrac{1}{99}\right)=0\Leftrightarrow x=100\)