Question

\(Cho\)\(a,b\in Z,b>0.\)\(So\)\(sánh\)HAI SỐ HỮU TỈ \(\frac{a}{b}\)VÀ \(\frac{a+2001}{b+2001}\)

Answer 1

\(\frac{a}{b}=1\Rightarrow\frac{a}{b}=\frac{a+2001}{b+2001}\)

\(\frac{a}{b}>1\Rightarrow\frac{a}{b}-1=\frac{a-b}{b}>\frac{a-b}{b+2001}=\frac{a+2001}{b+2001}-1\Rightarrow\frac{a}{b}>\frac{a+2001}{b+2001}\)

\(\frac{a}{b}< 1\Rightarrow a< b\Rightarrow1-\frac{a}{b}=\frac{b-a}{b}>\frac{b-a}{b+2001}=1-\frac{a+2001}{b+2001}\Rightarrow\frac{a}{b}< \frac{a+2001}{b+2001}\)

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