try and factor out x off one of the numerators or denominators (e.g. x + 3), its impossible right, so you will never get rid of x from the whole fraction
But take this example:
(x+2)/(x+7)
x and x cancel out, x/x = 1
= (1+2)/(1+7)
= 3/8
Am I misunderstanding something? It seems logical