\(\frac{x+5}{2005}+\frac{x+6}{2004}+\frac{x+7}{2003}=-3\)

\(\frac{x+5}{2005}+\frac{x+6}{2004}+\frac{x+7}{2003}+3=0\)

\(\left(\frac{x+5}{2005}+1\right)+\left(\frac{x+6}{2004}+1\right)+\left(\frac{x+7}{2003}+1\right)=0\)

\(\frac{x+5+2005}{2005}+\frac{x+6+2004}{2004}+\frac{x+7+2003}{2003}=0\)

\(\frac{x+2010}{2005}+\frac{x+2010}{2004}+\frac{x+2012}{2003}=0\)

\(\left(x+2010\right)\left(\frac{1}{2005}+\frac{1}{2006}+\frac{1}{2007}\right)=0\)

\(x+2010=0\)

\(x=-2010\)

\(\frac{x-1}{2005}+\frac{x-2}{2004}-\frac{x-3}{2003}=\frac{x-4}{2002}\)

=>\(\frac{x-1}{2005}+\frac{x-2}{2004}-\frac{x-3}{2003}-\frac{x-4}{2004}=0\)

=>\(\left(\frac{x-1}{2005}-1\right)+\left(\frac{x-2}{2004}-1\right)-\left(\frac{x-3}{2003}-1\right)-\left(\frac{x-4}{2002}-1\right)=0\)

=>\(\frac{x-1-2005}{2005}+\frac{x-2-2004}{2004}-\frac{x-3-2003}{2003}-\frac{x-4-2002}{2002}=0\)

=>\(\frac{x-2006}{2005}+\frac{x-2006}{2004}-\frac{x-2006}{2003}-\frac{x-2006}{2002}=0\)

=>\(\left(x-2006\right)\left(\frac{1}{2005}+\frac{1}{2004}-\frac{1}{2003}-\frac{1}{2002}\right)=0\)

Mà \(\frac{1}{2005}+\frac{1}{2004}-\frac{1}{2003}-\frac{1}{2002}\ne0\)

=> x - 2006 = 0 => x = 2006

c) 22/5 + 51/9 + 11/4 + 3/5 + 1/3 + 1/4
= 22/5 +3/5 +51/9 + 1/3 +11/4+1/4
= (22/5 +3/5) +(51/9 + 3/9) +(11/4+1/4)
= 25/5 +54/9 +12/4
= 5 +6 +3
= 14
d) (1/6 + 1/10 + 1/15) : (1/6 + 1/10 - 1/15) 
= (5/30 + 3/30 +2/30 ) :(5/30 +3/30 -2/30)
= 10/30 : 6/30
= 1/3 : 1/5
= 5/3

\(\frac{x+5}{2005}+1+\frac{x+6}{2004}+1+\frac{x+7}{2003}+1=0\)

<=> \(\frac{x+2010}{2005}+\frac{x+2010}{2004}+\frac{x+2010}{2003}=0\)

<=>\(\left(x+2010\right)\left(\frac{1}{2005}+\frac{1}{2004}+\frac{1}{2003}\right)=0\)

<=>x+2010=0

<=>x=-2010

Thái Hồ làm đúng rồi nhé Ngọc Vĩ . Bạn đó chuyển sang VT thành +3 rồi tách thành + 1 +1 +1 đó bạn. Bài của Ngọc Vĩ sai rồi

Thái Hồ làm đúng rùi !

\(P=\frac{\frac{1}{2003}+\frac{1}{2004}-\frac{1}{2005}}{\frac{5}{2003}+\frac{5}{2004}-\frac{5}{2005}}-\frac{\frac{2}{2002}+\frac{2}{2003}-\frac{2}{3004}}{\frac{3}{2002}+\frac{3}{2003}-\frac{3}{2004}}\)

\(\Rightarrow P=\frac{\frac{1}{2003}+\frac{1}{2004}-\frac{1}{2005}}{5\left(\frac{1}{2003}+\frac{1}{2004}-\frac{1}{2005}\right)}-\frac{2\left(\frac{1}{2002}+\frac{1}{2003}-\frac{1}{2004}\right)}{3\left(\frac{1}{2002}+\frac{1}{2003}-\frac{1}{2004}\right)}\)

\(\Rightarrow P=\frac{1}{5}-\frac{2}{3}\)

\(\Rightarrow P=\frac{3}{15}-\frac{10}{15}\)

\(\Rightarrow P=\frac{-7}{15}\)

Vậy \(P=\frac{-7}{15}\)

\(\frac{x+1}{1974}+\frac{x+2}{1973}+\frac{x+3}{1972}=-3\)

\(\Rightarrow\left(\frac{x+1}{1974}+1\right)+\left(\frac{x+2}{1973}+1\right)+\left(\frac{x+3}{1972}+1\right)=0\)

\(\Rightarrow\frac{x+1+1974}{1974}+\frac{x+2+1973}{1973}+\frac{x+3+1972}{1972}=0\)

\(\Rightarrow\frac{x+1975}{1974}+\frac{x+1975}{1973}+\frac{x+1975}{1972}=0\)

\(\Rightarrow\left(x+1975\right)\frac{1}{1974}+\frac{1}{1973}+\frac{1}{1972}=0\)

Mà \(\frac{1}{1974}+\frac{1}{1973}+\frac{1}{1972}\ne0\)

 \(\Rightarrow x+1975=0\)

\(\Rightarrow x=0+1975\)

\(\Rightarrow x=1975\)

Vậy \(x=1975\)

b) phần này làm tương tự phần a nha, chuyển -3 sang vế bên trái r cộng từng p.số vs 1 và sau đó nhóm tử số chung ra ngoài ^^

a)\(\left(\frac{2}{3}x-\frac{4}{9}\right).\left(\frac{1}{2}+\frac{-3}{7}:x\right)=0\)

\(\frac{2}{3}x-\frac{4}{9}=0\)hoặc\(\frac{1}{2}+\frac{-3}{7}:x=0\)

\(\frac{2}{3}x=\frac{4}{9}\)hoặc\(-\frac{3}{7}:x=-\frac{1}{2}\)

\(x=\frac{4}{9}:\frac{2}{3}\)hoặc\(x=-\frac{3}{7}:\frac{-1}{2}\)

\(x=\frac{2}{3}\)hoặc\(x=\frac{6}{7}\)

dễ mà bn,cộng 1 vào mỗi biểu thức và trừ vế 2 là xong

\(\frac{x+1}{2008}+\frac{x+2}{2007}+\frac{x+3}{2006}=\frac{x+4}{2005}+\frac{x+5}{2004}+\frac{x+6}{2003}\)

\(\Leftrightarrow\frac{x+1}{2008}+\frac{x+2}{2007}+\frac{x+3}{2006}+3=\frac{x+4}{2005}+\frac{x+5}{2004}+\frac{x+6}{2003}+3\)

\(\Leftrightarrow\left(\frac{x+1}{2008}+1\right)+\left(\frac{x+2}{2007}+1\right)+\left(\frac{x+3}{2006}+1\right)=\left(\frac{x+4}{2005}+1\right)\)

      \(+\left(\frac{x+5}{2004}+1\right)+\left(\frac{x+6}{2003}+1\right)\)

\(\Leftrightarrow\frac{x+2009}{2008}+\frac{x+2009}{2007}+\frac{x+2009}{2006}=\frac{x+2009}{2005}+\frac{x+2009}{2004}+\frac{x+2009}{2003}\)

\(\Leftrightarrow\frac{x+2009}{2008}+\frac{x+2009}{2007}+\frac{x+2009}{2006}-\frac{x+2009}{2005}-\frac{x+2009}{2004}-\frac{x+2009}{2003}=0\)

\(\Leftrightarrow\left(x+2009\right)\left(\frac{1}{2008}+\frac{1}{2007}+\frac{1}{2006}-\frac{1}{2005}-\frac{1}{2004}-\frac{1}{2003}\right)=0\)(1)

Vì \(\frac{1}{2008}+\frac{1}{2007}+\frac{1}{2006}-\frac{1}{2005}-\frac{1}{2004}-\frac{1}{2003}\ne0\)(2)

Từ (1) và (2) \(\Rightarrow x+2009=0\)\(\Rightarrow x=-2009\)

Vậy \(x=-2009\)

\(\frac{x+1}{2008}+\frac{x+2}{2007}+\frac{x+3}{2006}=\frac{x+4}{2005}+\frac{x+5}{2004}+\frac{x+6}{2003}\)

\(\Leftrightarrow\frac{x+1}{2008}+\frac{x+2}{2007}+\frac{x+3}{2006}+3=\frac{x+4}{2005}+\frac{x+5}{2004}+\frac{x+6}{2003}+3\)

\(\Leftrightarrow\left(\frac{x+1}{2008}+1\right)+\left(\frac{x+2}{2007}+1\right)+\left(\frac{x+3}{2007}+1\right)=\left(\frac{x+4}{2005}+1\right)+\left(\frac{x+5}{2004}+1\right)+\left(\frac{x+6}{2003}+1\right)\)

\(\Leftrightarrow\frac{x+2009}{2008}+\frac{x+2009}{2007}+\frac{x+2009}{2006}=\frac{x+2009}{2005}+\frac{x+2009}{2004}+\frac{x+2009}{2003}\)

\(\Rightarrow\left(x+2009\right)\left(\frac{1}{2008}+\frac{1}{2007}+\frac{1}{2006}\right)=\left(x+2009\right)\left(\frac{1}{2005}+\frac{2}{2004}+\frac{1}{2003}\right)\)

\(\Leftrightarrow\left(x+2009\right)\left(\frac{1}{2008}+\frac{1}{2007}+\frac{1}{2006}-\frac{1}{2005}-\frac{1}{2004}-\frac{1}{2003}\right)=0\)

\(\Rightarrow x+2009=0\)( Vì \(\frac{1}{2008}+\frac{1}{207}+\frac{1}{2006}-\frac{1}{2005}-\frac{1}{2004}-\frac{1}{2003}\ne0\))

=> x = -2009

x=-2007