Advanced MathVery hardSimplifying a cubic over a linear factor
Advanced Math practice question
For x ≠ 1, which expression is equivalent to (x³ − x)/(x − 1)?
- A. x² + xCorrect
- B. x² − 1
- C. x² + 1
- D. x² − x
Answer: A. x² + x
x³ − x = x(x² − 1) = x(x − 1)(x + 1). Cancel (x − 1): x(x + 1) = x² + x.
Why the other answers are wrong
- B. x² − 1
- x² − 1 cancels x instead of (x − 1), but the denominator is x − 1.
- C. x² + 1
- x² + 1 comes from a wrong division; check x = 2: (8 − 2)/1 = 6, but x² + 1 = 5.
- D. x² − x
- x² − x = x(x − 1) has the wrong sign; check x = 2: 2 ≠ 6.
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