[
  {
    "Question": "What is the simplified form of the rational expression (6x^2)/(9x^3)?",
    "Answer": "B",
    "Explanation": "To simplify the expression, divide both the numerator and the denominator by their greatest common factor, which is 3x^2. This results in (2)/(3x).",
    "PictureURL": "",
    "OptionA": "2/3",
    "OptionB": "2/(3x)",
    "OptionC": "2x/3",
    "OptionD": "2/(9x^2)",
    "OptionE": "",
    "OptionF": "",
    "OptionG": "",
    "TestName": "Rational Expressions Practice Test",
    "Content Type": "Mathematics",
    "Title": "Simplifying Rational Expressions",
    "Item": 1,
    "Type": "multiple choice",
    "Path": "Rational Expressions/Simplifying"
  },
  {
    "Question": "What is the result of multiplying the rational expressions (2/x) and (3/x^2)?",
    "Answer": "A",
    "Explanation": "To multiply rational expressions, multiply the numerators and the denominators separately. This gives (2*3)/(x*x^2) = 6/x^3.",
    "PictureURL": "",
    "OptionA": "6/x^3",
    "OptionB": "6/x^2",
    "OptionC": "6/x",
    "OptionD": "5/x^3",
    "OptionE": "",
    "OptionF": "",
    "OptionG": "",
    "TestName": "Rational Expressions Practice Test",
    "Content Type": "Mathematics",
    "Title": "Multiplying Rational Expressions",
    "Item": 2,
    "Type": "multiple choice",
    "Path": "Rational Expressions/Multiplying"
  },
  {
    "Question": "What is the sum of the rational expressions (1/2) + (1/3)?",
    "Answer": "C",
    "Explanation": "To add fractions, find a common denominator. The least common denominator of 2 and 3 is 6. Thus, (1/2) = (3/6) and (1/3) = (2/6). Adding these gives (3/6) + (2/6) = 5/6.",
    "PictureURL": "",
    "OptionA": "1/5",
    "OptionB": "5/6",
    "OptionC": "1/6",
    "OptionD": "1/3",
    "OptionE": "",
    "OptionF": "",
    "OptionG": "",
    "TestName": "Rational Expressions Practice Test",
    "Content Type": "Mathematics",
    "Title": "Adding Rational Expressions",
    "Item": 3,
    "Type": "multiple choice",
    "Path": "Rational Expressions/Adding"
  },
  {
    "Question": "What is the result of dividing the rational expression (4/x) by (2/x^2)?",
    "Answer": "B",
    "Explanation": "Dividing by a fraction is the same as multiplying by its reciprocal. Thus, (4/x) ÷ (2/x^2) = (4/x) * (x^2/2) = (4x)/(2) = 2x.",
    "PictureURL": "",
    "OptionA": "2/x",
    "OptionB": "2x",
    "OptionC": "2/x^2",
    "OptionD": "4/x",
    "OptionE": "",
    "OptionF": "",
    "OptionG": "",
    "TestName": "Rational Expressions Practice Test",
    "Content Type": "Mathematics",
    "Title": "Dividing Rational Expressions",
    "Item": 4,
    "Type": "multiple choice",
    "Path": "Rational Expressions/Dividing"
  },
  {
    "Question": "How do you solve the rational equation (x/2) = (3/x)?",
    "Answer": "A",
    "Explanation": "To solve the equation, cross-multiply to get x^2 = 6. Taking the square root gives x = ±√6. However, since x must be positive in this context, x = √6.",
    "PictureURL": "",
    "OptionA": "√6",
    "OptionB": "6",
    "OptionC": "3",
    "OptionD": "2",
    "OptionE": "",
    "OptionF": "",
    "OptionG": "",
    "TestName": "Rational Expressions Practice Test",
    "Content Type": "Mathematics",
    "Title": "Solving Rational Equations",
    "Item": 5,
    "Type": "multiple choice",
    "Path": "Rational Expressions/Solving"
  },
  {
    "Question": "What is an asymptote in the context of rational functions?",
    "Answer": "D",
    "Explanation": "An asymptote is a line that a graph approaches but never touches. Vertical asymptotes occur where the denominator is zero, while horizontal asymptotes describe the behavior as x approaches infinity.",
    "PictureURL": "",
    "OptionA": "A point where the graph intersects the x-axis",
    "OptionB": "A point where the graph intersects the y-axis",
    "OptionC": "A point of discontinuity",
    "OptionD": "A line the graph approaches but never touches",
    "OptionE": "",
    "OptionF": "",
    "OptionG": "",
    "TestName": "Rational Expressions Practice Test",
    "Content Type": "Mathematics",
    "Title": "Understanding Asymptotes",
    "Item": 6,
    "Type": "multiple choice",
    "Path": "Rational Expressions/Asymptotes"
  },
  {
    "Question": "What is the vertical asymptote of the function f(x) = (2)/(x-3)?",
    "Answer": "B",
    "Explanation": "Vertical asymptotes occur where the denominator is zero. Setting x - 3 = 0 gives x = 3 as the vertical asymptote.",
    "PictureURL": "",
    "OptionA": "x = 2",
    "OptionB": "x = 3",
    "OptionC": "x = 0",
    "OptionD": "x = -3",
    "OptionE": "",
    "OptionF": "",
    "OptionG": "",
    "TestName": "Rational Expressions Practice Test",
    "Content Type": "Mathematics",
    "Title": "Finding Vertical Asymptotes",
    "Item": 7,
    "Type": "multiple choice",
    "Path": "Rational Expressions/Asymptotes"
  },
  {
    "Question": "What is the horizontal asymptote of the function f(x) = (3x^2 + 2)/(4x^2 + 5)?",
    "Answer": "A",
    "Explanation": "For rational functions, the horizontal asymptote can be found by comparing the degrees of the numerator and denominator. Since both are degree 2, the horizontal asymptote is the ratio of the leading coefficients: 3/4.",
    "PictureURL": "",
    "OptionA": "y = 3/4",
    "OptionB": "y = 0",
    "OptionC": "y = 2",
    "OptionD": "y = 5",
    "OptionE": "",
    "OptionF": "",
    "OptionG": "",
    "TestName": "Rational Expressions Practice Test",
    "Content Type": "Mathematics",
    "Title": "Finding Horizontal Asymptotes",
    "Item": 8,
    "Type": "multiple choice",
    "Path": "Rational Expressions/Asymptotes"
  },
  {
    "Question": "What is the simplified form of the expression (x^2 - 1)/(x^2 - 2x + 1)?",
    "Answer": "C",
    "Explanation": "The numerator can be factored as (x - 1)(x + 1) and the denominator as (x - 1)(x - 1). Canceling the common factor (x - 1) gives (x + 1)/(x - 1).",
    "PictureURL": "",
    "OptionA": "(x + 1)/(x + 1)",
    "OptionB": "(x - 1)/(x - 1)",
    "OptionC": "(x + 1)/(x - 1)",
    "OptionD": "(x^2 - 1)/(x - 1)",
    "OptionE": "",
    "OptionF": "",
    "OptionG": "",
    "TestName": "Rational Expressions Practice Test",
    "Content Type": "Mathematics",
    "Title": "Simplifying Rational Expressions",
    "Item": 9,
    "Type": "multiple choice",
    "Path": "Rational Expressions/Simplifying"
  },
  {
    "Question": "If f(x) = (x + 2)/(x - 4), what is the value of f(4)?",
    "Answer": "D",
    "Explanation": "Substituting x = 4 into the function gives f(4) = (4 + 2)/(4 - 4) = 6/0, which is undefined. Therefore, f(4) does not exist.",
    "PictureURL": "",
    "OptionA": "6",
    "OptionB": "2",
    "OptionC": "4",
    "OptionD": "undefined",
    "OptionE": "",
    "OptionF": "",
    "OptionG": "",
    "TestName": "Rational Expressions Practice Test",
    "Content Type": "Mathematics",
    "Title": "Evaluating Rational Functions",
    "Item": 10,
    "Type": "multiple choice",
    "Path": "Rational Expressions/Evaluating"
  },
  {
    "Question": "What is the domain of the function f(x) = (1)/(x^2 - 9)?",
    "Answer": "C",
    "Explanation": "The domain of a rational function is all real numbers except where the denominator is zero. The denominator x^2 - 9 = 0 when x = ±3, so the domain is all real numbers except x = 3 and x = -3.",
    "PictureURL": "",
    "OptionA": "All real numbers",
    "OptionB": "x ≠ 3",
    "OptionC": "x ≠ 3 and x ≠ -3",
    "OptionD": "x ≠ 0",
    "OptionE": "",
    "OptionF": "",
    "OptionG": "",
    "TestName": "Rational Expressions Practice Test",
    "Content Type": "Mathematics",
    "Title": "Finding the Domain of Rational Functions",
    "Item": 11,
    "Type": "multiple choice",
    "Path": "Rational Expressions/Domain"
  },
  {
    "Question": "What is the result of (x^2 - 4)/(x + 2) when x = -2?",
    "Answer": "D",
    "Explanation": "Substituting x = -2 gives (-2^2 - 4)/(-2 + 2) = (4 - 4)/(0) = 0/0, which is undefined. Thus, the result is undefined.",
    "PictureURL": "",
    "OptionA": "0",
    "OptionB": "4",
    "OptionC": "2",
    "OptionD": "undefined",
    "OptionE": "",
    "OptionF": "",
    "OptionG": "",
    "TestName": "Rational Expressions Practice Test",
    "Content Type": "Mathematics",
    "Title": "Evaluating Rational Functions",
    "Item": 12,
    "Type": "multiple choice",
    "Path": "Rational Expressions/Evaluating"
  },
  {
    "Question": "What is the simplified form of (x^2 - 9)/(x - 3)?",
    "Answer": "A",
    "Explanation": "The numerator can be factored as (x - 3)(x + 3). Canceling the common factor (x - 3) gives x + 3.",
    "PictureURL": "",
    "OptionA": "x + 3",
    "OptionB": "x - 3",
    "OptionC": "x^2 - 3",
    "OptionD": "x + 9",
    "OptionE": "",
    "OptionF": "",
    "OptionG": "",
    "TestName": "Rational Expressions Practice Test",
    "Content Type": "Mathematics",
    "Title": "Simplifying Rational Expressions",
    "Item": 13,
    "Type": "multiple choice",
    "Path": "Rational Expressions/Simplifying"
  },
  {
    "Question": "What is the least common denominator (LCD) of the fractions (1/4) and (1/6)?",
    "Answer": "B",
    "Explanation": "The least common denominator of 4 and 6 is 12, as it is the smallest number that both denominators can divide into evenly.",
    "PictureURL": "",
    "OptionA": "6",
    "OptionB": "12",
    "OptionC": "24",
    "OptionD": "4",
    "OptionE": "",
    "OptionF": "",
    "OptionG": "",
    "TestName": "Rational Expressions Practice Test",
    "Content Type": "Mathematics",
    "Title": "Finding the Least Common Denominator",
    "Item": 14,
    "Type": "multiple choice",
    "Path": "Rational Expressions/LCD"
  },
  {
    "Question": "Which of the following is a characteristic of rational functions?",
    "Answer": "C",
    "Explanation": "Rational functions can have vertical and horizontal asymptotes, which are key characteristics that describe their behavior.",
    "PictureURL": "",
    "OptionA": "They are always linear",
    "OptionB": "They cannot have asymptotes",
    "OptionC": "They can have vertical and horizontal asymptotes",
    "OptionD": "They are always increasing",
    "OptionE": "",
    "OptionF": "",
    "OptionG": "",
    "TestName": "Rational Expressions Practice Test",
    "Content Type": "Mathematics",
    "Title": "Characteristics of Rational Functions",
    "Item": 15,
    "Type": "multiple choice",
    "Path": "Rational Expressions/Characteristics"
  }
]