Question

Which of the following is equal to the rational expression when x ≠ -1 or -7?

(X+1)(x-1)
——————
(X+7)(x+1)

A. x+1
——
x+7

B. x+7
———
x-1

C. x-1
——
x+7

Answer 1

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Answer:

C. (x -1)/(x +7)

Explanation:

The factor (x +1) in the numerator cancels the same factor in the denominator, leaving the ratio (x -1)/(x +7). This matches choice C.

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Additional comment

Even though (x+1)/(x+1) = 1 and can be removed from the expression, the fact that it is undefined at x=-1 means the reduced ratio (x-1)/(x+7) is only a valid representation of the original ratio when x≠-1. The factor (x+1) may be gone, but the domain restriction associated with it remains.