\(\dfrac{3-x}{100}-1=\dfrac{2-x}{101}+\dfrac{1-x}{102}\)

\(\Leftrightarrow\dfrac{3-x}{100}-\dfrac{100}{100}=\dfrac{102\left(2-x\right)}{101\cdot102}+\dfrac{101\left(1-x\right)}{101\cdot102}\)

\(\Rightarrow\dfrac{3-x-100}{100}=\dfrac{204-102x+101-101x}{10302}\)

\(\Rightarrow\dfrac{3-x-100}{100}=\dfrac{204+101-102x-101x}{10302}\)

\(\Rightarrow\dfrac{-97-x}{100}=\dfrac{305-203x}{10302}\)

=> 10302[-97 - x] = 100[305 - 203x]

=> -999294 - 10302x = 30500 - 20300x

=> -999294 - 30500 = - 20300x + 10302x

=> -1029794 = -9998x

=> x = 103

So x = 103

\(\dfrac{3-x}{100}-1=\dfrac{2-x}{101}+\dfrac{1-x}{102}\)

\(\Leftrightarrow\dfrac{3-x}{100}+1=\dfrac{2-x}{101}+1+\dfrac{1-x}{102}+1\)

\(\Leftrightarrow\dfrac{103-x}{100}-\dfrac{103-x}{101}-\dfrac{103-x}{102}=0\)

\(\Leftrightarrow\left(103-x\right)\left(\dfrac{1}{100}-\dfrac{1}{101}-\dfrac{1}{102}\right)=0\)

We have: \(\dfrac{1}{100}-\dfrac{1}{101}-\dfrac{1}{102}\ne0\)

\(\Rightarrow103-x=0\Rightarrow x=103\)