Advanced MathVery hardSimplifying a rational expression with a repeated factor
Advanced Math practice question
For x ≠ 2, the expression (3x² − 12)/(x² − 4x + 4) is equivalent to a(x + 2)/(x − 2), where a is a constant. What is the value of a?
Answer: 3
3x² − 12 = 3(x − 2)(x + 2) and x² − 4x + 4 = (x − 2)². Cancelling one (x − 2) leaves 3(x + 2)/(x − 2).
Common wrong answers
- If you answered 1
- 1 forgets the factor 3 pulled out of the numerator.
- If you answered 12
- 12 copies the constant from the numerator.
- If you answered -3
- −3 has the wrong sign.
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