Advanced MathHardConstant in a simplified rational expression
Advanced Math practice question
For x ≠ 0 and x ≠ −3, the expression (x² − 9)/(x² + 3x) is equivalent to (x − a)/x, where a is a constant. What is the value of a?
Answer: 3
Factor: (x − 3)(x + 3) over x(x + 3). Cancel (x + 3) to get (x − 3)/x, so a = 3.
Common wrong answers
- If you answered 0
- 0 would mean the expression equals 1, which is false (try x = 1: −8/4).
- If you answered 9
- 9 is the constant in the numerator before factoring; after cancelling, the numerator is x − 3.
- If you answered -3
- −3 would give (x + 3)/x, which keeps the factor that was cancelled.
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