50.7k views
3 votes
If x, y, a and b are greater than zero and x/y lessthanorequalto a/b, prove that x+a/y+b lessthanorequalto a/b

User Aniket V
by
8.2k points

1 Answer

4 votes

Answer:

Explanation:

Given x,y,a&b are greater than zero

also
(x)/(y)
\leq
(a)/(b)

since x,y,a&b are greater than zero therefore we can cross multiply them without changing the inequality

therefore


(x)/(a)
\leq
(y)/(b)

adding 1 on both sides we get


(x)/(a)+1
\leq
(y)/(b)+1


(x+a)/(a)
\leq
(y+b)/(b)

rearranging


(x+a)/(y+b)
\leq
(a)/(b)

User Apelsoczi
by
7.6k points