Question

Tìm x biết

\(\frac{x-1}{2004}+\frac{x-2}{2003}-\frac{x-3}{2002}\)\(=\frac{x-4}{2001}\)

 

Answer 1

\(\frac{x-1}{2004}+\frac{x-2}{2003}-\frac{x-3}{2002}=\frac{x-4}{2001}\)

=>\(\frac{x-1}{2004}-1+\frac{x-2}{2003}-1-\frac{x-3}{2002}-1=\frac{x-4}{2001}-1\)

=> \(\frac{x-1-2004}{2004}+\frac{x-2-2003}{2003}-\frac{x-3-2002}{2002}=\frac{x-4-2001}{2001}\)

=> \(\frac{x-2005}{2004}+\frac{x-2005}{2003}-\frac{x-2005}{2002}=\frac{x-2005}{2001}\)

=> \(\frac{x-2005}{2004}+\frac{x-2005}{2003}-\frac{x-2005}{2002}-\frac{x-2005}{2001}=0\)

=> \(\left(x-2005\right)\left(\frac{1}{2004}+\frac{1}{2003}-\frac{1}{2002}-\frac{1}{2001}\right)=0\)

Do \(\frac{1}{2004}+\frac{1}{2003}-\frac{1}{2002}-\frac{1}{2001}\ne0\)

=> x - 2005 = 0 => x = 2005