Finding simpler forms by cancellation of common factors

If you have a common factor in the numerator and the denominator of a fraction you can simplify by canceling the common factors (note that if you are working with rational functions this may change the domain and hence the function, though it will not change any values where both functions are defined-this is an important subtlety in calculus which may have been glossed over in your algebra class):

$$\frac{ac}{bc}=\frac{a}{b}$$

Note that if there are several terms in either numerator or denominator you need to make sure you have the factor in all of them:

$$\begin{array}{c}\frac{(x^2-4)^2 3x 2 - (3x^2-8)(x^2-4)}{(x^... ...)}{(x^2-4)^4}=\ \frac{6x^3-24x -3x^2 +8}{(x^2-4)^3}\end{array}$$

A common error is to take the factor only from the first term.