Advanced MathHardReducing a rational expression with a perfect square
Advanced Math practice question
For x ≠ 2 and x ≠ −2, which expression is equivalent to (x² − 4x + 4)/(x² − 4)?
- A. (x − 2)/(x + 2)Correct
- B. (x + 2)/(x − 2)
- C. (x − 2)²
- D. 1
Answer: A. (x − 2)/(x + 2)
The numerator is (x − 2)² and the denominator is (x − 2)(x + 2); one factor of x − 2 cancels.
Why the other answers are wrong
- B. (x + 2)/(x − 2)
- This cancels the wrong factor.
- C. (x − 2)²
- This ignores the denominator.
- D. 1
- The numerator and denominator are not equal.
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