Algebra 2 Practice Test: Rational Expressions
- Rational Expressions
- 10 questions
- 15 minutes
These 10 questions practice simplifying rational expressions, finding excluded values, multiplying, dividing, adding and subtracting them, and simplifying complex fractions. Factor every numerator and denominator first, then cancel only whole factors, never single terms.
Tap an option to mark your answer. You can change your mind, or tap the same option again to leave the question blank. The correct answers and explanations appear when you finish the test.Tap an option to answer; tap it again to leave the question blank.
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Question 1
Simplify x2 − 16x2 + 2x − 8.
Correct answer: A
Factor: (x − 4)(x + 4)(x + 4)(x − 2). Cancel the common factor x + 4 to get x − 4x − 2. Canceling the x2 terms is not allowed because they are terms, not factors.
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Question 2
Simplify x2 − 92x · 4x2x + 3.
Correct answer: C
(x − 3)(x + 3)2x · 4x2x + 3 = 4x2(x − 3)2x = 2x(x − 3).
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Question 3
Simplify x + 5x − 1 ÷ x2 + 5xx2 − 1.
Correct answer: A
Multiply by the reciprocal: x + 5x − 1 · (x − 1)(x + 1)x(x + 5) = x + 1x. Multiplying without flipping the second fraction gives the long expression instead.
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Question 4
Which expression is equivalent to 5x − 2 − 3x + 2?
Correct answer: D
Use the common denominator (x − 2)(x + 2): 5(x + 2) − 3(x − 2) = 5x + 10 − 3x + 6 = 2x + 16. Forgetting that −3 · (−2) = +6 gives 2x + 4.
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Question 5
For which values of x is x + 1x2 − 5x + 6 undefined?
Correct answer: B
The expression is undefined where the denominator is 0: x2 − 5x + 6 = (x − 2)(x − 3) = 0 at x = 2 and x = 3. A zero numerator at x = −1 only makes the value 0.
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Question 6
What is the least common denominator of 16x2 and 54x3?
Correct answer: A
The LCD uses the least common multiple of 6 and 4, which is 12, and the highest power of x, which is x3. Multiplying the denominators gives 24x5, a common denominator but not the least one.
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Question 7
Simplify the complex fraction 1 + 1x1 − 1x2.
Correct answer: C
The numerator is x + 1x and the denominator is (x − 1)(x + 1)x2. Dividing gives x + 1x · x2(x − 1)(x + 1) = xx − 1.
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Question 8
Simplify 3 − xx2 − 9.
Correct answer: B
Write 3 − x as −(x − 3). Then −(x − 3)(x − 3)(x + 3) = −1x + 3. Treating 3 − x and x − 3 as the same factor loses the minus sign.
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Question 9
Simplify 2xx + 1 + 2x + 1.
Correct answer: B
The denominators already match: 2x + 2x + 1 = 2(x + 1)x + 1 = 2 for x ≠ −1. Adding the denominators as well is the common mistake.
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Question 10
Simplify xx − 4 + 44 − x.
Correct answer: D
Since 4 − x = −(x − 4), the second fraction is −4x − 4. Then x − 4x − 4 = 1 for x ≠ 4.
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