How do you simplify #(z^2+x-1)/(z^2-3z+2)# and find the excluded values?
- 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
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:
#z^2-3z+2" "=" "(z-2)(z-1)#
So, without factoring the numerator, our expression is now
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
You can write this in math as follows: