Question

Let x,y,a and b be positive real numbers and not equal to 0. Assume that (x/y) < (a/b). Show that (x/y) < (x+a)/(y+b) .
Analysis problem. Please help. Thanks!

Answer 1

x and y or a and b have no value?

Answer 2

x/y < a/b)

add x/b both sides :
x/y + x/b < (a+x)/b

Answer 3

next, factor out x/y in left hand side :

x/y(1 + y/b) < (a+x)/b

x/y(b+y) < a+x

x/y < (a+x)/(b+y)

Answer 4

Thanks! So much that was so much simpler than I was trying to make it!!

Answer 5

if u got the answer then close it