Advanced MathHardDifference of two rational expressions that reduces to a constant
Advanced Math practice question
For x ≠ −1 and x ≠ 2, the expression (x² − 1)/(x + 1) − (x² − 4)/(x − 2) is equal to a constant. What is that constant?
Answer: -3
(x² − 1)/(x + 1) = x − 1 and (x² − 4)/(x − 2) = x + 2. Their difference is (x − 1) − (x + 2) = −3.
Common wrong answers
- If you answered 3
- 3 has the wrong sign.
- If you answered -1
- −1 forgets the +2 in the second simplified expression.
- If you answered -5
- −5 comes from (x − 1) − (x + 4), taking (x² − 4)/(x − 2) as x + 4.
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