16Hit1600
Advanced MathVery hardConstant from a partial-fraction style identity

Advanced Math practice question

For x ≠ 2, the expression (x² − 4)/(x − 2) + k is equal to x + 7 for every such x, where k is a constant. What is the value of k?

Answer: 5

(x² − 4)/(x − 2) = (x − 2)(x + 2)/(x − 2) = x + 2. So x + 2 + k = x + 7 and k = 5.

Common wrong answers

If you answered 3
3 would give x + 5, not x + 7; the fraction simplifies to x + 2, so k must be 5.
If you answered 7
7 forgets that the fraction already simplifies to x + 2, not x.
If you answered -5
−5 has the wrong sign.

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