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Equivalent Expressions Flashcards

7 cards from real Bluebook SAT Test practice questions. Tap to flip, then mark Knew It or Still Learning — missed cards come back until you master them.

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  1. Which of the following is equivalent to (2/(x+3)) + (5/(x+3))?

    Answer: 7/(x+3)

    Same denominator (x+3), so add numerators: (2+5)/(x+3) = 7/(x+3).

  2. Which of the following is equivalent to (x/(x+2)) − (2/(x+2))?

    Answer: (x−2)/(x+2)

    Same denominator (x+2): subtract numerators to get (x−2)/(x+2).

  3. Which of the following is equivalent to (x^5 · x^−2) / x?

    Answer: x²

    Numerator: x^(5+(−2)) = x³; divide by x¹: x^(3−1) = x².

  4. Which expression is equivalent to 4x² + 12x + 9?

    Answer: (2x + 3)²

    This is a perfect square trinomial: (2x)²+2(2x)(3)+3² = (2x+3)².

  5. Which of the following is equivalent to (x + y)² − 2xy?

    Answer: x² + y²

    Expand (x+y)² = x²+2xy+y²; subtract 2xy to get x²+y².

  6. Which of the following is equivalent to (6a²b³)/(3ab⁴)?

    Answer: 2a/b

    Divide coefficients: 6/3=2; divide variables: a^(2−1)=a, b^(3−4)=b^(−1)=1/b; result: 2a/b.

  7. Which of the following is equivalent to −(x − 4)² + 16?

    Answer: All of the above

    Expand −(x−4)² = −x²+8x−16; add 16: −x²+8x = −x(x−8) = x(8−x); all three are equivalent.