Final answer:
Subtract (z²)/(z-2) - (4)/(z-2) by subtracting numerators directly and simplifying, resulting in the final simplified answer of z + 2.
Step-by-step explanation:
To subtract the expressions (z²)/(z-2) and (4)/(z-2), we can make use of the fact that they have a common denominator. With the same denominator, we can subtract the numerators directly:
(z²)/(z-2) - (4)/(z-2)
= (z² - 4)/(z-2)
Now, we can simplify the numerator (z² - 4), recognizing it as the difference of two squares:
(z² - 4) = (z + 2)(z - 2)
Inserting this into the original equation gives us:
(z² - 4)/(z-2) = [(z + 2)(z - 2)]/(z-2)
Since (z - 2) appears in both numerator and denominator, we can cancel it out assuming z ≠ 2 to avoid division by zero:
[(z + 2)(z - 2)]/(z-2) = z + 2
Thus, the simplified expression is simply z + 2, which is our simplified answer.