The side splitter theorem exists as a ratio. In our case, [tex] \frac{NK}{KM} = \frac{NL}{LO} [/tex]. Filling it in with segment lengths, we have [tex] \frac{x+2}{x-3}= \frac{x}{x-4} [/tex]. Cross multiplying gives us [tex] x^{2} -2x-8= x^{2} -3x[/tex]. When we manipulate that equation the squared terms are eliminated, which is nice, leaving us with x-8=0 or x = 8
