Advanced MathMediumSimplifying by factoring both parts
Advanced Math practice question
For x ≠ 0 and x ≠ −3, which expression is equivalent to (x² − 9)/(x² + 3x)?
- A. (x − 3)/xCorrect
- B. (x + 3)/x
- C. (x − 3)/(x + 3)
- D. −3/x
Answer: A. (x − 3)/x
Factor: x² − 9 = (x − 3)(x + 3) and x² + 3x = x(x + 3). Cancel (x + 3): (x − 3)/x.
Why the other answers are wrong
- B. (x + 3)/x
- (x + 3) is the factor that cancels; (x − 3) is the one that remains.
- C. (x − 3)/(x + 3)
- (x − 3)/(x + 3) cancels the x instead of the (x + 3); but x is not a factor of x² − 9.
- D. −3/x
- −3/x 'cancels' the x² terms, which isn't valid: only common FACTORS cancel.
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