Question

cho a,b thuộc Z ,b>0. So sánh 2 số hữu tỉ \(\frac{a}{b}\) và \(\frac{a+2001}{b+2001}\)

Answer 1

Nếu 

a < b 

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

Nếu a > b 

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

Nếu a = b 

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

Answer 2

Xét tích            \(a\left(b+2001\right)=ab+2001a\\ b\left(a+2001\right)=ab+2001b.\)Vì \(b>0\)nên \(b+2001>0\).

Nếu \(a>b\) thì \(ab+2001a>ab+2001b\\ a\left(b+2001\right)>b\left(a+2001\right)\)

\(\frac{\Rightarrow a}{b}>\frac{a+2001}{b+2001}\) 

Nếu \(a< b\) thì \(\frac{\Rightarrow a}{b}< \frac{a+2001}{b+2001}\)

Nếu \(a=b\) thì rõ ràng \(\frac{a}{b}=\frac{a+2001}{b+2001}\)

Answer 3

= nhau