If x > 3, which of the following is equivalent to {1}{1/x+2 + 1/x+3}

Correct Answer is : x2+5x+62x+5x²+5x+6/2x+52x+5x2+5x+6

Correct Answer is : x2+5x+62x+5x²+5x+6/2x+52x+5x2+5x+6

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SATMathematics Practice Test 1

Question : 13 of 58

Marks: +1, -0

x > 3

\frac{1}{\frac{1}{x+2} + \frac{1}{x+3}}

Solution:

To rewrite

\frac{1}{\frac{1}{x+2} + \frac{1}{x+3}}

multiply by

\frac{(x+2)(x+3)}{(x+2)(x+3)}

This result in the expression

\frac{(x+2)(x+3)}{(x+3)(x+2)}

, which is equivalent to the expression in choice B.

Choices A, C, and D are incorrect and could be the result of common algebraic errors that arise while manipulating a complex fraction.

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