Question

Cho a,b thuộc Z , a< 0, b>0. So sánh hai số hữu tỉ a/b và (a + 2012) / (b + 2012)

Answer 1

Ta có:\(\frac{a}{b}=\frac{a.\left(b+2012\right)}{b.\left(b+2012\right)}=\frac{ab+a.2012}{b.\left(b+2012\right)}\)

\(\frac{a+2012}{b+2012}=\frac{b.\left(a+2012\right)}{b.\left(b+2012\right)}=\frac{ab+b.2012}{b.\left(b+2012\right)}\)

Vì a<0<b=>a<b=>a.2012<b.2012

=>\(\frac{ab+a.2012}{b.\left(b+2012\right)}