Question

cho a,b,c thuộc Z, b > 0

So sánh a/b và a+2001/b+2001

 

Answer 1

Có : \(\frac{a}{b}=\frac{a\left(b+2001\right)}{b\left(b+2001\right)}=\frac{ab+2001a}{b\left(b+2001\right)}\)

        \(\frac{a+2001}{b+2001}=\frac{\left(a+2001\right)b}{\left(b+2001\right)b}=\frac{ab+2001b}{b\left(b+2001\right)}\)

Vì b > 0 => b + 2001 > 0 => b(b+2001) > 0

+ Nếu a < b => ab + 2001a < ab + 2001b => \(\frac{ab+2001a}{b\left(b+2001\right)}< \frac{ab+2001b}{b\left(b+2001\right)}\Rightarrow\frac{a}{b}< \frac{a+2001}{b+2001}\)

+ Nếu a < b => ..............................................................................................................=> \(\frac{a}{b}>\frac{a+2001}{b+2001}\)

+ Nếu a = b => \(\frac{a}{b}=\frac{a+2001}{b+2001}\)