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Simplifying Rational Functions With Holes

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Let ff be the rational function defined by f(x)=(x+4)(x−2)(x+4)(x+1)f(x) = \frac{(x + 4)(x - 2)}{(x + 4)(x + 1)}. Which of the following is an equivalent representation of the function ff?

A

f(x)=x+4x+1f(x) = \frac{x + 4}{x + 1} for x≠−4x \neq -4

B

f(x)=x−2x+4f(x) = \frac{x - 2}{x + 4} for x≠−1x \neq -1

C

f(x)=x−2x+1f(x) = \frac{x - 2}{x + 1} for x≠−4x \neq -4

D

f(x)=x−2x+1f(x) = \frac{x - 2}{x + 1} for x≠−1x \neq -1

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