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Test
Math
Domain
Advanced Math
Skill
Equivalent expressions
Difficulty
Hard
ID: 89fc23af
Modded SAT Question Bank by Abdullah Mallik

Which of the following expressions is equivalent to the fraction with numerator x squared, minus 2 x, minus 5, and denominator x minus 3 ?

  1. x minus 5, minus the fraction with numerator 20, and denominator x minus 3

  2. x minus 5, minus the fraction with numerator 10, and denominator x minus 3

  3. x plus 1, minus the fraction with numerator 8, and denominator x minus 3

  4. x plus 1, minus the fraction with numerator 2, and denominator x minus 3


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Correct Answer: D
Rationale

Choice D is correct. The numerator of the given expression can be rewritten in terms of the denominator, x minus 3, as follows: x squared, minus 2 x, minus 5, equals, x squared, minus 3 x, plus x, minus 3, minus 2, which is equivalent to x times, open parenthesis, x minus 3, close parenthesis, plus, open parenthesis, x minus 3, close parenthesis, minus 2. So the given expression is equivalent to the fraction with numerator x times, open parenthesis, x minus 3, close parenthesis, plus, open parenthesis, x minus 3, close parenthesis, minus 2, and denominator x minus 3, end fraction, equals, the fraction with numerator x times, open parenthesis, x minus 3, close parenthesis, and denominator x minus 3, end fraction, plus the fraction with numerator x minus 3, and denominator x minus 3, end fraction, minus the fraction with numerator 2, and denominator x minus 3, end fraction. Since the given expression is defined for x is not equal to 3, the expression can be rewritten as x plus 1, minus, the fraction with numerator 2, and denominator x minus 3, end fraction.

Long division can also be used as an alternate approach. Choices A, B, and C are incorrect and may result from errors made when dividing the two polynomials or making use of structure.

 

Question Difficulty: Hard
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