# How do you simplify #(z^2+x-1)/(z^2-3z+2)# and find the excluded values?

##### 1 Answer

- Factor both numerator and denominator (separately).
- Reduce (if possible) by cancelling out common factors.
- To find excluded values, set the denominator of the expression (from step 1) equal to zero; solve for
#z# .

#### Explanation:

When simplifying a fraction such as this, we always want to start by **factoring the numerator and denominator**. Multiplicative factors may divide out, and they certainly help us find the excluded values.

Let's start with the numerator:

Next, we look at the denominator: *can* easily find two numbers that add to -3 and multiply to 2—those numbers are -2 and -1. We can then factor the denominator as follows:

#z^2-3z+2" "=" "(z-2)(z-1)#

So, without factoring the numerator, our expression is now

#(z^2+x-1)/((z-2)(z-1))#

In this form, it is easy to deduce the excluded values, because *an excluded value is any value for the variable which makes the expression undefined*, such as values that create division by zero. So we look at our denominator and see if there are any

Since our denominator is now written as a product of two factors, *it will only equal 0 when one of the factors is 0.* (In math terms, if the product **set each of the (denominator) factors equal to 0 and solve for #z#.**

You can write this in math as follows:

If

then

Both

#z!=1, 2# .