Advanced MathHardSimplifying a rational expression by factoring
Advanced Math practice question
For x ≠ −3, which expression is equivalent to (2x² + 6x) / (x + 3)?
- A. 2xCorrect
- B. 2x + 6
- C. 2x² + 2
- D. 2x + 2
Answer: A. 2x
Factor the numerator: 2x² + 6x = 2x(x + 3). The (x + 3) cancels with the denominator (allowed because x ≠ −3), leaving 2x.
Why the other answers are wrong
- B. 2x + 6
- 2x + 6 is what remains if you cancel only the x from x + 3 against the x² — but cancellation works on whole factors, and (x + 3) is the factor here.
- C. 2x² + 2
- Dividing each term by 3 instead of by (x + 3) gives nothing sensible; the denominator is a binomial and must be treated as a unit.
- D. 2x + 2
- 2x + 2 would need the numerator to factor as (x + 3)(2x + 2) = 2x² + 8x + 6, which it doesn't.
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