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  3. For each of Questions 1 to 9, compare Quantity A and Quantity B, using additional information centered above the two quantities

For each of Questions 1 to 9, compare Quantity A and Quantity B, using additional information centered above the two quantities

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问题 For each of Questions 1 to 9, compare Quantity A and Quantity B, using additional information centered above the two quantities if such information is given. Select one of the following four answer choices and fill in the corresponding oval to the right of the question.
(A)Quantity A is greater.
(B)Quantity B is greater.
(C)The two quantities are equal.
(D)The relationship cannot be determined from the information given.
A symbol that appears more than once in a question has the same meaning throughout the question.

选项
答案B
解析 One approach you could use to solve this problem is to solve the equation for x. Since fractions are defined only when the denominator is not equal to 0, the denominators of both of the fractions in the equation are nonzero. Therefore, x0 and x1.
    To solve the equation for x, begin by multiplying both sides of the "equation by the common denominator x(x + 1)to get x(l - x)=(x - 1)(1). Then proceed as follows.
x(1 -x)=(x- 1)(1)
x - x2 = x - 1
x2=1
Since x2= 1 and x1, it follows that x = -1.
    Quantity A is equal to -1 and Quantity B is equal to. Therefore, Quantity B is greater, and the correct answer is Choice B.
    Another approach is to notice that for all values of x1, the value ofis equal to -1. You can try plugging in a few numbers for x to see that this is true. For example, if you plug in x = 7, you get=-1.
    You can also show that for all values of x1, the value ofis equal to -1 algebraically by rewriting 1 - x as -(x - 1). Thus,= -1. Because the left side of the equationis equal to -1, it follows that -1 = 1/x, and so x = -1. Therefore, Quantity A is equal to -1, which is less than Quantity B,, and the correct answer is Choice B.
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