ACT Math · Polynomial and rational functions
For which values of x is x-2/x+1 > 0?
For which values of is ?
Answer and explanation
Answer: D: x 2
The expression changes sign at the critical points x=−1 and x=2. Testing each interval: for x<−1, both (x−2) and (x+1) are negative, giving a positive quotient. For −1<x<2, the quotient is negative. For x>2, both factors are positive, giving a positive quotient. The solution is x<−1 or x>2. Choice A describes the interval where the expression is negative, not positive.
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