what are the excluded values for 2x-8 over x^2-6x+8 ?

Question

When finding the domain of a rational expression the excluded values are any values of the variable that makes the expression undefined.
^{what are the excluded values for 2x-8 over x2-6x+8}








What would be the excluded values in the simplified form of the expression?









A student says that you can divide out 8 and x from the expression in part a to simplify the expression. Is this statement correct? If not identify the error in their reasoning.

Answer 1

Hi Brooke,

To start you should get the factors of the numerator and denominator of the expression

the numerator would have the factors 2 and (x-4)

the denominator would have the factors (x-4) and (x-2)

now excluded values are values that make your denominator equal to zero.

 

So our denominator will be zero when either of the factors is zero

 

x - 4 = 0    or x=4

x - 2 = 0    or x=2

 

so 4 and 2 are excluded from the domain

 

in the simplified expression, we can factor (x-4) out of the numerator and denominator  and we are left with only (x-2) in the denominator.

 

so for the simplified expression,  when x-2 = 0   or x = 2 we have an excluded value

 

Hope this helps

 

Tom