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Rational Expressions

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The following math revision questions are provided in support of the math tutorial on Rational Expressions. In addition to this tutorial, we also provide revision notes, a video tutorial, revision questions on this page (which allow you to check your understanding of the topic) and calculators which provide full, step by step calculations for each of the formula in the Rational Expressions tutorials. The Rational Expressions calculators are particularly useful for ensuring your step-by-step calculations are correct as well as ensuring your final result is accurate.

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Polynomials Learning Material
Tutorial IDTitleTutorialVideo
Tutorial		Revision
Notes		Revision
Questions
11.4Rational Expressions

Rational Expressions Revision Questions

1. . Which of the following is NOT a rational expression?

  1. 3/2x
  2. x - 1/2x
  3. 1/√x
  4. 5

Correct Answer: C

2. . What is the rational expression form of

√x - 1/x√x - x
  1. 1
  2. x - 1
  3. 1/x
  4. x

Correct Answer: C

3. . Which of the following is a disallowed value for the rational expression

x2 - 5x + 4/2x2 - 8x + 6
  1. -1
  2. 4
  3. 0
  4. 3

Correct Answer: D

4. . What is the simplest form of the rational expression

36x2 y3/9x2 yz
  1. 4y2z
  2. 4y2/z
  3. 4xy/z
  4. 27y2/z

Correct Answer: B

5. . Which of the following is equivalent to the rational expression

x2 - 1/2x - 2
  1. x + 1/2
  2. x - 1/2
  3. x - 1/x + 1
  4. x + 1/2(x - 1)

Correct Answer: A

6. . What is

x - 1/3x + 2/9x
  1. 3x - 1/3x
  2. 3x - 1/9x
  3. 3x + 1/3x
  4. 3x - 5/3x

Correct Answer: A

7. . What is

x - 2/3x - 2x - 1/1 - x
  1. 1 - x/4x - 1
  2. 7x2 - 6x + 2/3x2 - 3x
  3. 2x2 - 5x + 2/-3x2 + 3x
  4. 2x2 - 5x + 2/2x - 1

Correct Answer: B

8. . Write the product below in the simplest form

2x2 + 7x - 4/10x - 5 ∙ 12 - 3x/x3 - 16x
  1. -3/5
  2. -3/5x
  3. -3x/5
  4. 3/5

Correct Answer: B

9. . Calculate

x + 1/x ÷ 2x + 2/4x2
  1. 2x
  2. 1/2x
  3. 2x2
  4. 2/x

Correct Answer: A

10. . What is the LCM of 6x3y4z and 8xy2z4?

  1. 14x4y6z5
  2. 24x4y6z5
  3. 24 x3y4z4
  4. 24xyz

Correct Answer: C

11. . What is the simplest form of the complex fraction

3 - x/2x/x - 3/12x
  1. -6
  2. 6
  3. -x2 + 9/24x
  4. -x2 - 9/24x

Correct Answer: A

12. . What is the value of

5 - 5 - 5 - .../3/3
  1. 14/3
  2. 15/4
  3. 16/5
  4. 17/6

Correct Answer: B

More challenging questions

13. . What is the simplest form of the following complex fraction

x + 1 + 1 + 1/x/x + 1/x/1/x
  1. 3/x
  2. x + 1/x
  3. 4x
  4. 3x

Correct Answer: D

14. . If we have

7x - 6/x2 - x - 6 = A/x - 3 + B/x + 2

then what is A · B

Hint! You have to solve a system of linear equations with A and B as variables.

  1. 3
  2. 4
  3. 12
  4. 15

Correct Answer: C

15. . If

x2 - y2 = 36 and 1/x + y + 1/x - y = 5/9

are given, then what is the value of y?

  1. 4
  2. 6
  3. 8
  4. 10

Correct Answer: C

Whats next?

Enjoy the "Rational Expressions" practice questions? People who liked the "Rational Expressions" practice questions found the following resources useful:

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  2. Polynomials Math tutorial: Rational Expressions. Read the Rational Expressions math tutorial and build your math knowledge of Polynomials
  3. Polynomials Video tutorial: Rational Expressions. Watch or listen to the Rational Expressions video tutorial, a useful way to help you revise when travelling to and from school/college
  4. Polynomials Revision Notes: Rational Expressions. Print the notes so you can revise the key points covered in the math tutorial for Rational Expressions
  5. Check your calculations for Polynomials questions with our excellent Polynomials calculators which contain full equations and calculations clearly displayed line by line. See the Polynomials Calculators by iCalculator™ below.
  6. Continuing learning polynomials - read our next math tutorial: The Definition of Monomials and Polynomials

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