Advanced MathHardDifference of two squared expressions with a reciprocal
Advanced Math practice question
For x ≠ 0, what is the value of (x + 1/x)² − (x − 1/x)²?
Answer: 4
Expand: (x² + 2 + 1/x²) − (x² − 2 + 1/x²) = 4, for every nonzero x. (Or use a² − b² = (a − b)(a + b) = (2/x)(2x) = 4.)
Common wrong answers
- If you answered 0
- 0 assumes the two squares are equal; they differ in the middle term.
- If you answered 2
- 2 counts the middle term once instead of twice.
- If you answered 4x
- The result does not depend on x; the x terms cancel.
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