SAT Math Multiple Choice Question 889: Answer and Explanation

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Test Information

Question: 889


Which of the following is equivalent to the rational expression given above?

  • A.
  • B.
  • C.
  • D.

Correct Answer: C



Difficulty: Hard

Category: Passport to Advanced Math / Exponents

Strategic Advice: When adding fractions, you need to find a common denominator, even when the fractions contain variables. Factor the denominators to find the least common denominator (LCD).

Getting to the Answer: The original expression, after factoring each of the denominators, is. The least common denominator is x(x + 3)(x + 1). Multiply each numerator and each denominator by whatever is missing from the LCD in that particular term (the first term is missing the x + 1, and the second term is missing the x + 3). Then simplify each numerator as much as possible, and add the results by combining like terms:

This doesn't match any of the answer choices, so try to reduce further. Factor the numerator to get. You can divide the factor (x + 3) from the numerator and denominator to get, which matches (C).

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