I want to expand on what the tutor @greenestamps wrote when he said the following
(1) The numerator is monotonically increasing;
(2) The denominator is monotonically decreasing
Therefore, the function is monotonically increasing.
The idea is this:
Consider a number C = A/B where B is nonzero.
If A goes up and B goes down, then C goes up
Example:
A = 12
B = 2
A/B = 12/2 = 6
A+1 = 12+1 = 13
B-1 = 2-1 = 1
We have C = A/B = 12/2 = 6 turn into C = (A+1)/(B-1) = 13/1 = 13
In short we have gone from 6 to 13 to show an overall increase.
This one example to show the claim above is correct. That claim being the overall function is monotonically increasing.
A more rigorous proof is required to fully verify the claim of course, but the example hopefully helps illustrate what is going on.
Monotonic means the function is always moving in one direction. Though the graph may have some sub-intervals as flat. This is where the graph is neither increasing nor decreasing.
In some math textbooks, the requirement is that there aren't any flat portions. However, the same idea applies in that the curve is either always going upward or always going downward.
A non-example of a monotonic function would be something like y = x^2. The left half decreases while the right side increases. The entire curve itself isn't doing the same thing over the domain.