Question

cho a,b,c thuộc  Nsao.CMR nếu;

a,\(\frac{a}{b}\)bé hơn 1 thì\(\frac{a}{b}\)+\(\frac{a+n}{b+n}\)

b,\(\frac{a}{b}\)lớn hơn 1 thì \(\frac{a}{b}\) bé hơn \(\frac{a+n}{b+n}\)

Answer 1

\(\frac{a}{b}< \frac{a+n}{b+n}\) \(\left(1\right)\)

\(\Leftrightarrow a\left(b+n\right)< b\left(a+n\right)\)

\(\Leftrightarrow ab+an< ab+bn\)

\(\Leftrightarrow an< bn\)

\(Do.a< b\)nên an<bn\(\Rightarrow\)(1)

\(\frac{a}{b}>\frac{a+n}{b+n}\)\(\left(2\right)\)

\(\Leftrightarrow a\left(b+n\right)>b\left(a+n\right)\)

\(\Leftrightarrow ab+an>ab+bn\)

\(\Leftrightarrow an>bn\)

Do a>b nên \(\Rightarrow\)(2)