a,\(\dfrac{2-x}{2001}-1=\dfrac{1-x}{2002}-\dfrac{x}{2003}\)
<=> \(\dfrac{2-x}{2001}-1+2=\dfrac{1-x}{2002}-\dfrac{x}{2003}+2\)
<=>\(\dfrac{2-x}{2001}+1=\left(\dfrac{1-x}{2002}+1\right)+\left(\dfrac{-x}{2003}+1\right)\)
<=>\(\dfrac{2003-x}{2001}=\dfrac{2003-x}{2002}+\dfrac{2003-x}{2003}\)
<=>\(\dfrac{2003-x}{2001}-\dfrac{2003-x}{2002}-\dfrac{2003-x}{2003}=0\)
<=> \(\left(2003-x\right)\left(\dfrac{1}{2001}-\dfrac{1}{2002}-\dfrac{1}{2003}\right)=0\)
Vì \(\dfrac{1}{2001}-\dfrac{1}{2002}-\dfrac{1}{2003}\ne0\)
=> \(2003-x=0\)
=> \(x=2003\)
Vậy : S = \(\left\{2003\right\}\)
b, \(\dfrac{2x-3}{97}-\dfrac{2x-4}{96}+\dfrac{2x-5}{95}=\dfrac{2x-6}{94}\)
<=> \(\dfrac{2x-3}{97}-\dfrac{2x-4}{96}=\dfrac{2x-6}{94}-\dfrac{2x-5}{95}\)
<=> \(\dfrac{2x-3}{97}-\dfrac{2x-4}{96}-2=\dfrac{2x-6}{94}-\dfrac{2x-5}{95}-2\)
<=> \(\left(\dfrac{2x-3}{97}-1\right)-\left(\dfrac{2x-4}{96}-1\right)=\left(\dfrac{2x-6}{94}-1\right)-\left(\dfrac{2x-5}{95}-1\right)\)
<=>\(\dfrac{2x-100}{97}-\dfrac{2x-100}{96}=\dfrac{2x-100}{94}-\dfrac{2x-100}{95}\)
<=> \(\dfrac{2x-100}{97}-\dfrac{2x-100}{96}-\dfrac{2x-100}{94}+\dfrac{2x-100}{95}=0\)
<=> \(\left(2x-100\right)\left(\dfrac{1}{97}-\dfrac{1}{96}-\dfrac{1}{94}+\dfrac{1}{95}\right)=0\)
Vì \(\dfrac{1}{97}-\dfrac{1}{96}-\dfrac{1}{94}+\dfrac{1}{95}\ne0\)
=>\(2x-100=0\)
=> \(2x=100\)
=>\(x=50\)
Vậy: S=\(\left\{50\right\}\)
