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Ta có :
\(\frac{x+4}{2000}+\frac{x+3}{2001}=\frac{x+2}{2002}+\frac{x+1}{2003}\)
\(\Rightarrow\frac{x+4}{2000}+1+\frac{x+3}{2001}+1=\frac{x+2}{2002}+1+\frac{x+1}{2003}+1\)
\(\Rightarrow\frac{x+2004}{2000}+\frac{x+2004}{2001}=\frac{x+2004}{2002}+\frac{x+2004}{2003}\)
\(\Rightarrow\frac{x+2004}{2000}+\frac{x+2004}{2001}-\frac{x+2004}{2002}-\frac{x+2004}{2003}=0\)
\(\Rightarrow\left(x+2004\right)\left(\frac{1}{2000}+\frac{1}{2001}-\frac{1}{2002}-\frac{1}{2003}\right)=0\)
Mà \(\frac{1}{2000}+\frac{1}{2001}-\frac{1}{2002}-\frac{1}{2003}\ne0\)
\(\Rightarrow x+2004=0\)
\(\Rightarrow x=-2004\)
Vậy ...
=>x+4/2000+1+x+3/2001+1=x+2/2002+1+x+1/2003+1
=>x+2004/2000+x+2004/2001=x+2004/2002+x+2004/2003
=>(x+2004)(1/2000+1/2001-1/2002-1/2003)=0
=>x+2004=0
=>x=-2004
Giải bài khó nhất =)
\(\frac{x+4}{2000}+\frac{x+3}{2001}=\frac{x+2}{2002}+\frac{x+1}{2003}\)
\(\Leftrightarrow\left(\frac{x+4}{2000}+1\right)+\left(\frac{x+3}{2001}+1\right)=\left(\frac{x+2}{2002}+1\right)+\left(\frac{x+1}{2003}+1\right)\)
\(\Leftrightarrow\frac{x+2004}{2000}+\frac{x+2004}{2001}=\frac{x+2004}{2002}+\frac{x+2004}{2003}\)
\(\Leftrightarrow\frac{x+2004}{2000}+\frac{x+2004}{2001}-\frac{x+2004}{2002}-\frac{x+2004}{2003}=0\)
\(\Leftrightarrow\left(x+2004\right)\left(\frac{1}{2000}+\frac{1}{2001}+\frac{1}{2002}+\frac{1}{2003}\right)=0\)
Do \(\frac{1}{2000}+\frac{1}{2001}+\frac{1}{2002}+\frac{1}{2003}\ne0\) nên \(x+2004=0\Leftrightarrow x=-2004\)
\(\frac{x+4}{2000}+\frac{x+3}{2001}=\frac{x+2}{2002}+\frac{x+1}{2003}\)
\(\Leftrightarrow\left(\frac{x+4}{2000}+1\right)+\left(\frac{x+3}{2001}+1\right)=\left(\frac{x+2}{2002}+1\right)+\left(\frac{x+1}{2003}+1\right)\) (cộng cả 2 vế với 2)
\(\Leftrightarrow\)\(\frac{x+2004}{2000}+\frac{x+2004}{2001}=\frac{x+2004}{2002}+\frac{x+2004}{2003}\)
\(\Leftrightarrow\left(x+2004\right)\left(\frac{1}{2000}+\frac{1}{2001}-\frac{1}{2002}-\frac{1}{2003}\right)=0\)
\(\Leftrightarrow x+2004=0\)
\(\Leftrightarrow x=2004\)
\(\frac{x+4}{2000}+\frac{x+3}{2001}=\frac{x+2}{2002}+\frac{x+1}{2003}\)
<=> \(\frac{x+4}{2000}+1+\frac{x+3}{2001}+1=\frac{x+2}{2002}+1+\frac{x+1}{2003}+1\)
<=> \(\left(x+2004\right)\left(\frac{1}{2000}+\frac{1}{2001}-\frac{1}{2002}-\frac{1}{2001}\right)=0\)
<=> x+2004=0
<=> x=-2004
\(\frac{x+4}{2000}+\frac{x+3}{2001}=\frac{x+2}{2002}+\frac{x+1}{2003}\)
\(\left(\frac{x+4}{2000}+1\right)+\left(\frac{x+3}{2001}+1\right)=\left(\frac{x+2}{2002}+1\right)+\left(\frac{x+1}{2003}+1\right)\)
\(\left(\frac{x+4}{2000}+\frac{2000}{2000}\right)+\left(\frac{x+3}{2001}+\frac{2001}{2001}\right)=\left(\frac{x+2}{2002}+\frac{2002}{2002}\right)+\left(\frac{x+1}{2003}+\frac{2003}{2003}\right)\)
\(\frac{x+2004}{2000}+\frac{x+2004}{2001}=\frac{x+2004}{2002}+\frac{x+2004}{2003}\)
\(\frac{x+2004}{2000}+\frac{x+2004}{2001}-\frac{x+2004}{2002}-\frac{x+2004}{2003}=0\)
\(x+2004\left(\frac{1}{2000}+\frac{1}{2001}-\frac{1}{2002}-\frac{1}{2003}\right)=0\)
Ta thấy \(\frac{1}{2000}>\frac{1}{2001}>\frac{1}{2002}>\frac{1}{2003}\)
nên \(\left(\frac{1}{2000}+\frac{1}{2001}+\frac{1}{2002}+\frac{1}{2003}\right)\ne0\)
Do đó: x + 2004 = 0 => x = -2004
Vậy x = -2004
\(\frac{x+4}{2000}+\frac{x+3}{2001}=\frac{x+2}{2002}+\frac{x+1}{2003}\)
\(\Rightarrow\frac{x+4}{2000}+1+\frac{x+3}{2001}+1=\frac{x+2}{2002}+1+\frac{x+1}{2003}+1\)
\(\Rightarrow\frac{x+2004}{2000}+\frac{x+2004}{2001}-\frac{x+2004}{2002}-\frac{x+2004}{2003}=0\)
\(\Leftrightarrow\left(x+2004\right)\left(\frac{1}{2000}+\frac{1}{2001}-\frac{1}{2002}-\frac{1}{2003}\right)=0\)
Vì \(\frac{1}{2000}+\frac{1}{2001}-\frac{1}{2002}-\frac{1}{2003}\ne0\)
Nên x + 2004 = 0
=> x = -2004
Vậy x = -2004
\(\frac{x-1}{2004}+\frac{x-2}{2003}-\frac{x-3}{2002}=\frac{x-4}{2001}\)
\(\Rightarrow\frac{x-1}{2004}+\frac{x-2}{2003}-\frac{x-3}{2002}-\frac{x-4}{2001}=0\)
\(\Rightarrow\frac{x-1}{2004}-1+\frac{x-2}{2003}-1-\frac{x-3}{2002}+1-\frac{x-4}{2001}+1=0\)
\(\Rightarrow\left(\frac{x-1}{2004}-1\right)+\left(\frac{x-2}{2003}-1\right)-\left(\frac{x-3}{2002}-1\right)-\left(\frac{x-4}{2001}-1\right)=0\)
\(\Rightarrow\frac{x-2005}{2004}+\frac{x-2005}{2003}-\frac{x-2005}{2002}-\frac{x-2005}{2001}=0\)
\(\Rightarrow\left(x-2005\right).\left(\frac{1}{2004}+\frac{1}{2003}-\frac{1}{2002}-\frac{1}{2001}\right)=0\)
Vì \(\frac{1}{2004}< \frac{1}{2002};\frac{1}{2003}< \frac{1}{2001}\)\(\Rightarrow\frac{1}{2004}+\frac{1}{2003}-\frac{1}{2002}-\frac{1}{2001}\ne0\)
\(\Rightarrow x-2005=0\)
\(\Rightarrow x=2005\)
Vậy x = 2005
vào vào đây http://olm.vn/hoi-dap/question/113906.html
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Có \(\frac{x+4}{2000}\) + \(\frac{x+3}{2001}\) = \(\frac{x+2}{2002}\) + \(\frac{x+1}{2003}\)
( \(\frac{x+4}{2000}\) + 1 ) + ( \(\frac{x+3}{2001}\) + 1 ) = ( \(\frac{x+2}{2002}\) + 1 ) + ( \(\frac{x+1}{2003}\) + 1 )
( \(\frac{x+4}{2000}\) + \(\frac{2000}{2000}\) ) + ( \(\frac{x+3}{2001}\) + \(\frac{2001}{2001}\) ) = ( \(\frac{x+2}{2002}\) + \(\frac{2002}{2002}\) ) + ( \(\frac{x+1}{2003}\) + \(\frac{2003}{2003}\) )
\(\frac{x+4+2000}{2000}\) + \(\frac{x+3+2001}{2001}\) = \(\frac{x+2+2002}{2002}\) + \(\frac{x+1+2003}{2003}\)
\(\frac{x+2004}{2000}\) + \(\frac{x+2004}{2001}\) = \(\frac{x+2004}{2002}\) + \(\frac{x+2004}{2003}\)
\(\frac{x+2004}{2000}\) + \(\frac{x+2004}{2001}\) - \(\frac{x+2004}{2002}\) - \(\frac{x+2004}{2003}\) = 0
( x + 2004 ) + ( \(\frac{1}{2000}\) + \(\frac{1}{2001}\) + \(\frac{1}{2002}\) + \(\frac{1}{2003}\) ) = 0
Mà \(\frac{1}{2000}\) + \(\frac{1}{2001}\) + \(\frac{1}{2002}\) + \(\frac{1}{2003}\) \(\ne\) 0
\(\Rightarrow\) x + 2004 = 0
\(\Rightarrow\) x = -2004
Vậy x = - 2014