Question

Cho a,b \(\varepsilon Z,b>0\)

Hãy so sanh \(\frac{a}{b}và\frac{a+2001}{b+2001}\)

Answer 1

b>0 nen b+2001 >0

Xet 1-a/b =(b-a)/b

1-(a+2001)/(b+2001)=(b-a)/(b+2001)

Nếu a=b thì (b-a)/b=(b-a)/(b+2001)=0

=>1-a/b=1-(a+2001)/(b+2001)

Neu a>b thi b-a < 0 

=>(b-a)/b < (b-a)/(b+2001)

<=>1-a/b < 1-(a+2001)/(b+2001)

<=>a/b> (a+2001)/(b+2001)

Neu a < b thi b-a >0

=>(b-a)/b > (b-a)/(b+2001)

<=>1 - a/b > 1-(a+2001)/(b+2001)

<=>a/b < (a+2001)/(b+2001)