Question

So sánh cá phân số sau :

2010.2011/2010.2011+1 và 2009.2010/2009.2010+1

Answer 1

Ta có:

2010 . 2011/2010 . 2011 + 1                                                                      2009 . 2010/2009 . 2010 + 1

= 1 - 1/2010 . 2011 + 1                                                                             = 1 - 1/2009 . 2010 + 1

Vì 2010 . 2011 + 1 > 2009 . 2010 + 1

=> 1/2010 . 2011 + 1 < 1/2009 . 2010 + 1

=> 1 - 1/2010 . 2011 + 1 > 1 - 1/2009 . 2010 + 1

=> 2010.2011/2010.2011+1 > 2009.2010/2009.2010+1

Answer 2

lớn hơn á bạn

Answer 3

Ta có: \(2010\cdot2011>2009\cdot2010\)\(\Rightarrow2010\cdot2011+1>2009\cdot2010+1\)

\(\Rightarrow\frac{1}{2010\cdot2011+1}< \frac{1}{2009\cdot2010+1}\)

\(\Rightarrow-\frac{1}{2010\cdot2011+1}>-\frac{1}{2009\cdot2010+1}\)

\(\Rightarrow1-\frac{1}{2010\cdot2011+1}>1-\frac{1}{2009\cdot2010+1}\)

\(\Rightarrow\frac{2010\cdot2011+1-1}{2010\cdot2011+1}>\frac{2009\cdot2010+1-1}{2009\cdot2010+1}\)

\(\Rightarrow\frac{2010\cdot2011}{2010\cdot2011+1}>\frac{2009\cdot2010}{2009\cdot2010+1}\)(ĐPCM)