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Subtract, (z²)/(z-2) - (4)/(z-2) Simplify your answer as much as possibly

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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.

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