Toán 8 Giải phương trình [tex]\frac{x+1}{2012}+\frac{x+2}{2011}=\frac{x+3}{2010}+\frac{x+4}{2009}[/tex]

Mỗi số hạng cộng thêm 1 thì PT vẫn thỏa mãn, khi đó ta có:
[tex]\frac{x+2013}{2012}+\frac{x+2013}{2011}=\frac{x+2013}{2010}+\frac{x+2013}{2009}[/tex] <=>x=-2013

[tex]\frac{x+1}{2012}+\frac{x+2}{2011}=\frac{x+3}{2010}+\frac{x+4}{2009}[/tex]
[tex]<=>\frac{x+1}{2012}+1+\frac{x+2}{2011}+1=\frac{x+3}{2010}+1+\frac{x+4}{2009}+1[/tex]
[tex]<=>\frac{x+2013}{2012}+\frac{x+2013}{2011}=\frac{x+2013}{2010}+\frac{x+2013}{2009}[/tex]
[tex]<=>(x+2013)(\frac{1}{2012}+\frac{1}{2011}-\frac{1}{2010}-\frac{1}{2009})=0[/tex]
[tex]<=>x=-2013[/tex]