SAT Equivalent expressions Practice Question 13 (Medium)

Math · Advanced MathMedium

For $x \ne -4$ , the expression $\frac{2x^2 + 5x - 12}{x + 4}$ is equivalent to $ax + b$ , where $a$ and $b$ are constants. What is the value of $a - b$ ?

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Answer: 5

Factor the numerator: $2x^2 + 5x - 12 = (2x - 3)(x + 4)$ . Dividing by $x + 4$ leaves $2x - 3$ , so $a = 2$ and $b = -3$ . Then $a - b = 2 - (-3) = 5$ .

Taking $b = 3$ instead of $-3$ gives $a - b = -1$ .

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