# How do you simplify #(x^2-7x+12) / (x-4) #?

##### 1 Answer

You must factor the numerator to see if anything can eliminate itself.

#### Explanation:

To factor a trinomial of the form

=

Since dividing a number by itself gives one, the x - 4 in the numerator and the x - 4 in the denominator eliminate themselves. This leaves us with

The key for simplifying rational expressions: **always factor completely to see what you can eliminate!!**. Also, as you will see in the practice exercises, it is most helpful to factor out the GCF (greatest common factor) before engaging in other types of factorization.

**Practice exercises:**

- Simplify the following rational expressions.

a)

b)

c)

Good luck!