Advanced MathHardValue of a simplified rational expression
Advanced Math practice question
For x ≠ 2 and x ≠ −2, the expression (x² + 2x)/(x² − 4) simplifies to x/(x − k), where k is a constant. What is the value of k?
Answer: 2
x² + 2x = x(x + 2) and x² − 4 = (x − 2)(x + 2). Cancel (x + 2): x/(x − 2), so k = 2.
Common wrong answers
- If you answered 0
- 0 would give x/x = 1, which is false (try x = 1: 3/(−3) = −1).
- If you answered 4
- 4 is the constant in the original denominator.
- If you answered -2
- −2 would give x/(x + 2), keeping the cancelled factor.
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