x+8/x^2-4x

Question

Find the domain of the rational function.

 

Problem: x+8/x^2-4x

 

Answer 1

Let's factor out the denominator.

We need to do this because we cannot divide by 0:

x² - 4x ⇒ x(x - 4)

x = 0

 

x - 4 = 0

x = 4

 

Since x cannot be either of those numbers, we have for the domain "every value when x ≠ 0, 4."

Answer 2

(x + 8) / (x² - 4x)

 

 

The domain of a function is the x values where the function exists on a graph. 

 

 

Set the denominator of the rational function equal to zero.

 

x² - 4x = 0

 

x(x - 4) = 0

 

 

Set the factors of the denominator equal to zero.

 

x = 0             and            x - 4 = 0

                                       x = 4

 

The domain is  (-∞, 0)∪(0, 4)∪(4, ∞)