Rational Expressions Quiz

Grade 10 · Math · Quiz

Test your ability to simplify, operate on, and find domain restrictions for rational expressions.

Questions

  1. Which value is excluded from the domain of 5/(x² - 9)?

    1. x = 9
    2. x = 3 and x = -3
    3. x = 0
    4. x = 3 only
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    Answer: x = 3 and x = -3

    x²-9=(x-3)(x+3). Setting each factor to zero: x=3 and x=-3 are both excluded.

  2. Simplified form of (x² - 4)/(x + 2) is x - ___, where x ≠ -2.

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    Answer: 2

    (x²-4)=(x+2)(x-2). Canceling (x+2) leaves (x-2). The blank is 2.

  3. What is (3/x) × (x²/6)?

    1. x/2
    2. 2/x
    3. 3x/6
    4. 1/2x
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    Answer: x/2

    (3/x)(x²/6) = 3x²/(6x) = x/2 after canceling 3 and one x.

  4. The expression (x + 4)/(x + 4) simplifies to 1 for all values of x.

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    Answer: False

    (x+4)/(x+4)=1 only when x≠-4. At x=-4, the expression is undefined (0/0).

  5. What is (4/x) ÷ (2/x²)?

    1. 8/x³
    2. 2x
    3. 8x
    4. 2/x
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    Answer: 2x

    Dividing: (4/x)×(x²/2) = 4x²/(2x) = 2x.

  6. To subtract rational expressions with different denominators, first find the ___.

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    Answer: LCD

    A common denominator (the least common denominator) is required to combine fractions through addition or subtraction.

  7. Simplify: (2x² + 4x) / (2x)

    1. x + 4
    2. x + 2
    3. 2x + 4
    4. x² + 2
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    Answer: x + 2

    Factor numerator: 2x(x+2). Divide by 2x: result is (x+2). So the answer is x+2.

  8. When multiplying rational expressions, you must find a common denominator first.

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    Answer: False

    Multiplication: multiply numerators together and denominators together directly — no common denominator needed.

  9. The LCD of 1/(x-1) and 1/(x+2) is:

    1. (x-1)
    2. (x+2)
    3. (x-1)(x+2)
    4. (x-1)+(x+2)
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    Answer: (x-1)(x+2)

    The LCD is the product of the distinct factors: (x-1)(x+2), since they share no common factors.

  10. A rational expression can have more than one domain restriction.

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    Answer: True

    Any value making any factor of the denominator zero must be excluded. A denominator like (x-1)(x+2) excludes two values.

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