Explanation The given expression is x − 1 2 x + 5 . Since the above radical represents a real number the fraction under the radical is greater than or equal to zero. Solve the inequality x − 1 2 x + 5 ≥ 0 as follows. Setting each factors of numerator equal to zero the critical values are found as follows. ( x − 1 ) = 0 implies x = 1 , ( 2 x + 5 ) = 0 implies x = − 5 2 The critical values are x = 1 , x = − 5 2 . Now, determine the sign of the given function for each of the intervals x < − 5 2 , − 5 2 < x < 1 , and x > 1 . The sign of the function for corresponding intervals are tabulated as follows

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Chapter 17, Problem 58RE

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The value of x for which the radical x−12x+5 represents the real number.

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Chapter 17, Problem 57RE

Chapter 17, Problem 59RE

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The value of x for which the radical x − 1 2 x + 5 represents the real number.

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The value of x for which the radical x−12x+5 represents the real number.

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