\(\dfrac{x-1}{2011}+\dfrac{x-2}{2010}-\dfrac{x-3}{2009}=\dfrac{x-4}{2008}\)

<=> \(\left(\dfrac{x-1}{2011}-1\right)+\left(\dfrac{x-2}{2010}-1\right)-\left(\dfrac{x-3}{2009}-1\right)=\left(\dfrac{x-4}{2008}-1\right)\)

<=> \(\dfrac{x-2012}{2011}+\dfrac{x-2012}{2010}-\dfrac{x-2012}{2009}-\dfrac{x-2012}{2008}=0\)

<=> \(\left(x-2012\right)\left(\dfrac{1}{2011}+\dfrac{1}{2010}-\dfrac{1}{2009}-\dfrac{1}{2008}\right)=0\)

<=> x - 2012 = 0

<=> x = 2012

a) \(\frac{x+4}{2009}+1+\frac{x+3}{2010}+1=\frac{x+2}{2011}+1+\frac{x+1}{2012}\)

\(\frac{x+4+2009}{2009}+\frac{x+3+2010}{2010}=\frac{x+2+2011}{2011}+\frac{x+2+2012}{2012}\)

\(\frac{x+2013}{2009}+\frac{x+2013}{2010}-\frac{x+2013}{2011}-\frac{x+2013}{2012}=0\)

\(\left(x+2013\right).\left(\frac{1}{2009}+\frac{1}{2010}-\frac{1}{2011}-\frac{1}{2012}\right)=0\)    (1)

Vì \(\left(\frac{1}{2009}+\frac{1}{2010}-\frac{1}{2011}-\frac{1}{2012}\right)\ne0\)

Nên biểu thức (1) xảy ra khi \(x+2013=0\)

\(x=-2013\)

b) \(\left(x-2011\right)\left(\frac{1}{2010}+\frac{1}{2011}+\frac{1}{2012}-\frac{1}{2013}-\frac{1}{2014}\right)=0\)  (2)

Vì \(\left(\frac{1}{2010}+\frac{1}{2011}+\frac{1}{2012}-\frac{1}{2013}-\frac{1}{2014}\right)\ne0\)

Nên biểu thức (2) xảy ra khi \(x-2011=0\)

\(x=2011\)

X x 2011 - X x 1 = 2011 x 2 +2009

X x ( 2011 - 1 ) = 4022 + 2009

X x 2010 = 6031

      2010

X x 2011 - X = 2011 + 2009 + 2011

X x ( 2011 - 1 ) = 2011 x ( 2009 + 1 )

X x 2010 = 2011 x 2010 

X = 2011

x * 2011 - x = 2011 + 2009 + 2011

x * ( 2011 - 1 ) = 2011 * ( 2009 + 1 )

x * 2010 = 2011 x 2010

x = 2011

x=2011 hoặc x=-2010

8

bang 8 bạn tich nha

CẢM ƠN BẠN NHIỀU

x . 2011 - x = 2011 . 2009 - 2011

x.(2011 - 1) = 4038088

x . 2010 = 4038088

x = 4038088: 2010

x = 2008,999005

X x 2011-X = 2011 x 2009 - 2011

X x ( 2011-1)   = 2011 x (2009- 1)

X x 2010        = 2011 x 2010

=> X=2011

Tim giá trị biểu thức : A = 1/4+1/12+1/24+1/40+1/60+1/84

X x 2011 - X = 2011 x 2009 + 2011

=> X x ( 2011-1) = 2011 x (2009+1)

=> X x 2010 = 2011 x 2010

=> X = 2011