Advanced MathVery hardSimplifying a fraction with a negative exponent
Advanced Math practice question
For x > 0 and x ≠ 1, which expression is equivalent to (x⁻¹ − 1)/(1 − x)?
- A. 1/xCorrect
- B. −1/x
- C. x
- D. −1
Answer: A. 1/x
x⁻¹ − 1 = (1 − x)/x, and dividing by (1 − x) leaves 1/x.
Why the other answers are wrong
- B. −1/x
- The signs of numerator and denominator match, so the result is positive.
- C. x
- This inverts the correct answer.
- D. −1
- This forgets the factor of x in the denominator.
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