Proving Inequality: a/b < (a+1)/(b+1) for b > a | Solution and Attempt

[John H]

Homework Statement

Prove that if b is a positive number, such that a < b, then
a/b<(a+1)/(b+1)

2. The attempt at a solution

I have tried a few things, attempting to prove it using the real line, and a bunch of other methods but have had no success. I Would greatly appreciate it if u can at least get me started.

 

[Dick]

Homework Statement

Prove that if b is a positive number, such that a < b, then
a/b<(a+1)/(b+1)

2. The attempt at a solution

I have tried a few things, attempting to prove it using the real line, and a bunch of other methods but have had no success. I Would greatly appreciate it if u can at least get me started.

Clear out the fractions, i.e. multiply both sides by the common denominator. You didn't try that?

 

[John H]

I did before, but I made the most retarded mistake of thinking a(b+1)=b(a+1). Sorry about that. Thanx

 

[ehild]

a<b. You can add any number to both sides of an inequality, it stays valid. Why not trying to add ab?

ehild