vi \(\frac{-2009}{2010}>\frac{-2010}{1010}=1\)

\(\frac{2010}{-2009}=\frac{-2010}{2009}

x=y      

\(x=\frac{-17}{23}\)

\(y=\frac{-171717}{232323}=\frac{\left(-171717\right):10101}{232323:10101}=\frac{-17}{23}\)

\(\Rightarrow x=y\)

Ta có : 

\(17A=\frac{17^{2009}+17}{17^{2009}+1}=\frac{17^{1009}+1+16}{17^{2009}+1}=\frac{17^{2009}+1}{17^{2009}+1}+\frac{16}{17^{2009}+1}=1+\frac{16}{17^{2009}+1}\)

\(17B=\frac{17^{2010}+17}{17^{2010}+1}=\frac{17^{2010}+1+16}{17^{2010}+1}=\frac{17^{2010}+1}{17^{2010}+1}+\frac{16}{17^{2010}+1}=1+\frac{16}{17^{2010}+1}\)

Vì \(\frac{16}{17^{2009}+1}>\frac{16}{17^{2010}+1}\) nên \(17A>17B\)

\(\Rightarrow\)\(A>B\)

Vậy \(A>B\)

Chúc bạn học tốt ~ 

Ta co : 

y=-171717/232323=-17/23

Ma :-17/23=-17/23

Vay x=y

Đặt A = \(\frac{2009^{2009}+1}{2009^{2010}+1}\)

      B = \(\frac{2009^{2010}-2}{2009^{2011}-2}\)

Do 2009²⁰¹⁰- 2 < 2009²⁰¹¹- 2 => \(B<1\)

\(B=\frac{2009^{2010}-2}{2009^{2011}-2}<\frac{2009^{2010}-2+2011}{2009^{2011}-2+2011}=\frac{2009^{2010}+2009}{2009^{2011}+2009}=\frac{2009\left(1+2009^{2009}\right)}{2009\left(1+2009^{2010}\right)}\)

\(=\frac{2009^{2009}+1}{2009^{2010}+1}=A\Rightarrow\)B < A

nhân A 2009 lần và B 2009 lần mà so sánh

ta có:

B=(2009^2010-2)/(2009^2011-2)<1

=>(2009^2010-2)/(2009^2011-2)<(2009^2010-2)+2011/(2009^2011-2)+2011=(2009^2010+2009)/(2009^2011+2009)

=[2009*(2009^2009+1)]/[2009*(2009^2010+1)]=(2009^2009+1)/(2009^2010+1)=A

Vậy A=B

Đúng thì !