Advanced MathHardConstant in a simplified rational expression
Advanced Math practice question
For x ≠ 0 and x ≠ 4, (x² − 16)/(x² − 4x) is equivalent to (x + k)/x, where k is a constant. What is the value of k?
Answer: 4
Factor: (x − 4)(x + 4) over x(x − 4). Cancel (x − 4): (x + 4)/x, so k = 4.
Common wrong answers
- If you answered 0
- 0 would mean the expression equals 1, which is false (try x = 1: −15/−3 = 5).
- If you answered 16
- 16 is the constant in the original numerator, not after simplifying.
- If you answered -4
- −4 would give (x − 4)/x, keeping the cancelled factor.
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