\(\frac{x+4}{2000}+\frac{x+3}{2001}=\frac{x+2}{2002}+\)\(\frac{x+1}{2003}\)
\(\Leftrightarrow\left(\frac{x+4}{2000}+1\right)+\left(\frac{x+3}{2001}+1\right)\)\(=\left(\frac{x+2}{2002}+1\right)+\left(\frac{x+1}{2003}+1\right)\)
\(\Leftrightarrow\left(\frac{x+2004}{2000}\right)+\left(\frac{x+2004}{2001}\right)\)\(=\left(\frac{x+2004}{2002}\right)+\left(\frac{x+2004}{2003}\right)\)
\(\Leftrightarrow\left(x+2004\right)\)\(\left(\frac{1}{2000}+\frac{1}{2001}-\frac{1}{2002}-\frac{1}{2003}\right)\)\(=0\)
\(\Leftrightarrow x+2004=0\)
\(\Leftrightarrow x=-2004\)
x+4/2000 + x+3/2001 = x+2/2002 + x+1/2003
( x+4/2000 .+ 1) + (x+3/2001 + 1) = (x+2/2002 + 1) + (x+1/2003 + 1)
( x+4/2000 + 2000/2000) + (x+3/2001 + 2001/2001) = (x+2/2002 +2002/2002) + (x+1/2003 +2003/2003)
x+2004/2000 + x+2004/2001 = x+2004/2002 + x+2004/2003
= x+2004/2000 + x+2004/2001 - x+2004/2002 - x+2004/2003
-> (x+2004) .(1/2000 + 1/2001 -1/2002 -2/2003) = 0
-> x+2004 = 0
x = 0-2004
x = -2004
Vay x= -2004
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