\(\frac{x-2}{99}+\frac{x-3}{98}=\frac{x-4}{97}+\frac{x-5}{96}\Leftrightarrow\frac{x-2}{99}-1+\frac{x-3}{98}-1=\frac{x-4}{97}-1+\frac{x-5}{96}-1\)
<=>\(\frac{x-101}{99}+\frac{x-101}{98}=\frac{x-101}{97}+\frac{x-101}{96}\)
<=>\(\left(x-101\right)\left(\frac{1}{99}+\frac{1}{98}-\frac{1}{97}-\frac{1}{96}\right)=0\)
<=>x-101=0 \(\left(\frac{1}{99}+\frac{1}{98}-\frac{1}{97}-\frac{1}{96}\ne0\right)\)
<=>x=101