Advanced MathVery hardSubtracting rational conjugate fractions
Advanced Math practice question
For x ≠ 3 and x ≠ −3, the difference 1/(x − 3) − 1/(x + 3) equals a/(x² − 9) for a constant a. What is the value of a?
Answer: 6
Over the common denominator (x − 3)(x + 3) = x² − 9, the numerator is (x + 3) − (x − 3) = 6.
Common wrong answers
- If you answered 0
- The numerators differ: (x + 3) − (x − 3) = 6, not 0.
- If you answered 2
- The x-terms cancel but the constants add: 3 − (−3) = 6.
- If you answered -6
- Subtracting in the given order gives +6; −6 would come from reversing the fractions.
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