If a/b >1, and c is a positive integer, prove that a/b>(a+c)/(b+c) ?

2 Answers
Jul 22, 2017

See below.

Explanation:

Assuming a > 0, b > 0, if a/b > 1 rArr a > b then

ab + ac > ab + bc or

a(b + c) > b(a+c) rArr a/b > (a+c)/(b+c)

Jul 22, 2017

The assertion fails if a, b < 0

Explanation:

The assertion fails if a, b < 0

Consider a=-3, b=-2 and c=1

Then:

a/b = (-3)/(-2) = 3/2 > 1

(a+c)/(b+c) = (-3+1)/(-2+1) = (-2)/(-1) = 2 > 3/2