16Hit 1600
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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