What is the largest value?

X and Y are two different numbers selected from the first fifty counting numbers from 1 to 50 inclusive. What is the largest value that $\dfrac{X+Y}{X-Y}$ can have?

A fraction has largest value when numerator has the largest value possible and denominator has the smallest value possible. 

In this case, largest value possible for X+Y = 50+49 = 99
smallest value for X-Y = 50-49 = 1

 $\dfrac{X+Y}{X-Y}$ =  $\dfrac{99}{1}$ = 99

The largest value  $\dfrac{X+Y}{X-Y}$ can have is 99.