Bluebook SAT Test Equivalent Expressions 12

Question 1

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

Accepted Answer

7/(x+3)

Answer

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

Question 2

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

Accepted Answer

(x−2)/(x+2)

Answer

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

Question 3

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

Accepted Answer

x²

Answer

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

Question 4

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

Accepted Answer

(2x + 3)²

Answer

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

Question 5

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

Accepted Answer

x² + y²

Answer

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

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