A rational expression is of the form a/b, where a and b can be polynomials.

Cancelling like factors involves dividing both the numerator and denominator by the same expression to reduce the ratio to a simpler form. It does not change the value of the rational expression.

Example:

a = (x^2 - 1)

b = (x^2 +3x - 4)

Factoring these we get:

a = (x-1)(x+1)

b = (x-1)(x+4)

now a/b = {(x-1)(x+1)} / {(x-1)(x+4)}

Clearly we can remove (x-1) from both the numerator and denominator, doing so yields:

a/b = (x+1) / (x+4)

This should explain both the theory and practice of this method :)