Advanced MathVery hardProduct of rational expressions
Advanced Math practice question
For x ≠ 1 and x ≠ −1, which expression is equivalent to (x² − 1)/(x + 1) · 1/(x − 1)?
- A. 1Correct
- B. x − 1
- C. (x − 1)²
- D. 1/(x + 1)
Answer: A. 1
(x² − 1)/(x + 1) = x − 1, and (x − 1) · 1/(x − 1) = 1.
Why the other answers are wrong
- B. x − 1
- x − 1 stops after the first simplification, forgetting the multiplication by 1/(x − 1).
- C. (x − 1)²
- (x − 1)² multiplies by (x − 1) instead of dividing.
- D. 1/(x + 1)
- 1/(x + 1) cancels the wrong factor.
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