Question

Cho a, b, c \(\in\)N*. So sánh \(\frac{a+n}{b+n}\)và\(\frac{a}{b}\)

 

Answer 1

+) Nếu \(\frac{a}{b}< 1\)

=> a < b

=> an < bn

=> ab + an < ab + bn

=> a(b + n) < b(a + n)

=> \(\frac{a}{b}< \frac{a+n}{a+n}\)

+) Nếu \(\frac{a}{b}>1\)

=> a > b

=> an > bn

=> ab + an > ab + bn

=> a(b + n) > b(a + n)

=> \(\frac{a}{b}>\frac{a+n}{b+n}\)

Answer 2

+) Nếu \(\frac{a}{b}=1\)

=> a = b

=> a + n = b + n

=> \(\frac{a+n}{b+n}=\frac{a}{b}\)