SOLUTION: If b is a positive number and a < b (recall that this is another way of saying b-a>0), show that a/b < (a+1)/(b+1)

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Question 1015790: If b is a positive number and a < b (recall that this is another
way of saying b-a>0), show that a/b < (a+1)/(b+1)
Found 2 solutions by fractalier, Edwin McCravy:
Answer by fractalier(6550)   (Show Source): You can put this solution on YOUR website!
From

let us cross-multiply and get
a(b+1) < b(a+1)
ab + a < ab + b
Subtract off ab and get
a < b
which is what you supposed to be true to begin with...
Answer by Edwin McCravy(20062)   (Show Source): You can put this solution on YOUR website!
The other tutor's proof is wrong.  He proved the converse
of what you are to prove.  He started by assuming
the conclusion and proved what was given.  You must
start with what is given, not with what you are to
prove.   

Here is the correct proof:

If b is a positive number and a < b
show that 
We start with what is given,
(not with what we are to prove, as he did):



and use the hint:



We replace 0 by the equivalent ab - ab.



We add ab to both sides:
 


We add a to both sides



Factor out common factors on each side



Divide both sides by b+1, which is positive
since b is positive. Therefore we will not 
reverse the inequality when we divide by b+1:



Divide both sides by b which is positive and
also will not reverse the inequality when we 
divide by it:



which is equivalent to



Edwin
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