Xand y are two different numbers selected from the first fifty counting numbers from 1 to 50 inclusive.
what is the largest value that (x+y) / (x-y) can have?

In order to make a fraction as large as possible, you want the numerator to be large, and the denominator to be small.

Using the counting numbers, the smallest denominator (x - y) you can make is ' 1 '.
Now you just have to make the numerator large. You do that simply by using the largest two numbers you have available . . . 49 and 50 .

Now the fraction is (49 + 50) / 1 = 99 .

The largest value  will be for x=50 and y=49.