Question

[Trần Phương Nam]

So sánh 2 phân số:

A=2009*2009+2008/2009*2009+2009 va B=2009*2009+2009/2009*2009+2010

Answer 1

[Hoàng Phúc]

Vì 20009 x 2009 + 2008 < 2009 x 2009 + 2009

=>A < 1

Ta có: \(B=\frac{2009x2009+2009}{2008x2009+2010}=\frac{2009x\left(2008+1\right)+2009}{2008x2009+2010}=\frac{2008x2009+2009+2009}{2008x2009+2010}\)

\(B=\frac{2008x2009+4018}{2008x2009+2010}=\frac{2008x2009+2010+2008}{2008x2009+2010}=\frac{2008x2009+2010}{2008x2009+2010}+\frac{2008}{2008x2009+2010}\)

\(B=1+\frac{2008}{2008x2009+2010}>1\)

Mà A < 1

=>A < B

Answer 2

[Hoàng Phúc]

dòng đầu sửa chỗ 20009 nhé,2009