Advanced MathVery hardConstant in a rewritten rational expression
Advanced Math practice question
For all x ≠ −1, (2x − 3)/(x + 1) = 2 − k/(x + 1), where k is a constant. What is the value of k?
Answer: 5
2 − k/(x + 1) = (2x + 2 − k)/(x + 1); matching numerators gives 2 − k = −3, so k = 5.
Common wrong answers
- If you answered 1
- 1 solves 2 − k = 1.
- If you answered 3
- 3 copies the constant from the numerator.
- If you answered -5
- −5 has the sign wrong; the expression already subtracts k/(x + 1).
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