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Rational Expressions Practice Tests

These Grade 11 Math practice tests develop rational-expression skills across domains, restrictions, factoring, simplification, multiplication, division, addition, subtraction, complex fractions, rational equations, asymptotes, holes, and variation models.

Skills covered

  • Finding excluded values and domains from factored denominators
  • Simplifying rational expressions by factoring and canceling common factors without losing restrictions
  • Multiplying, dividing, adding, subtracting, and simplifying complex rational expressions
  • Solving rational equations with common denominators, checking for extraneous solutions, and interpreting asymptotes and holes
  • Applying direct variation \(y=kx\), inverse variation \(y=\frac{k}{x}\), rational graphs, units, and contextual reasonableness

How to use these practice tests

Write denominator restrictions before simplifying. Factor completely, use a common denominator or reciprocal as appropriate, and substitute candidate solutions into the original expression or equation.

For more Grade 11 Math practice, return to the Grade 11 Math category.

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5 Tests
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1. Test

Grade 11 Rational Expressions Practice Tests

Practice Grade 11 Math questions about rational-expression domains, simplification, operations, rational equations, asymptotes, holes, direct variation, and inverse variation.

Choose the best answer. Factor before canceling, record denominator restrictions, use common denominators or reciprocals, and check every solution in the original equation.

10 Questions
0/10 Questions0 %
Correct 0
Incorrect 0
Unanswered 10
1. QuestionMultiple choice

For what value is 1x−5\frac{1}{x-5} undefined?

Please select an answer first.

Correct answer: A

The correct answer is x=5x=5.

  1. Identify the rational-expression structure: Determine the denominators, restrictions, common factors, operation, or equation involved.
  2. Apply the algebraic relationship: A rational expression is undefined when its denominator is zero, so x - 5 = 0 gives x = 5.
  3. Check restrictions and the result: The correct answer is x=5x=5.

A rational expression is undefined when its denominator is zero, so x - 5 = 0 gives x = 5.

2. QuestionMultiple choice

What is the domain of x+2x2−9\frac{x+2}{x^2-9}?

Please select an answer first.

Correct answer: B

The correct answer is All real numbers except x=−3x=-3 and x=3x=3.

  1. Identify the rational-expression structure: Determine the denominators, restrictions, common factors, operation, or equation involved.
  2. Apply the algebraic relationship: Factor x^2 - 9 as (x - 3)(x + 3), so both denominator zeros are excluded.
  3. Check restrictions and the result: The correct answer is All real numbers except x=−3x=-3 and x=3x=3.

Factor x^2 - 9 as (x - 3)(x + 3), so both denominator zeros are excluded.

3. QuestionMultiple choice

Simplify x2−16x−4\frac{x^2-16}{x-4} for x≠4x\ne4.

Please select an answer first.

Correct answer: C

The correct answer is x+4x+4.

  1. Identify the rational-expression structure: Determine the denominators, restrictions, common factors, operation, or equation involved.
  2. Apply the algebraic relationship: Factor x^2 - 16 as (x - 4)(x + 4) and cancel the common factor while keeping x = 4 excluded.
  3. Check restrictions and the result: The correct answer is x+4x+4.

Factor x^2 - 16 as (x - 4)(x + 4) and cancel the common factor while keeping x = 4 excluded.

4. QuestionMultiple choice

What is the greatest common factor of 6x2+9x3x\frac{6x^2+9x}{3x}?

Please select an answer first.

Correct answer: D

The correct answer is 3x3x.

  1. Identify the rational-expression structure: Determine the denominators, restrictions, common factors, operation, or equation involved.
  2. Apply the algebraic relationship: Both numerator terms share 3x, so 6x^2 + 9x = 3x(2x + 3).
  3. Check restrictions and the result: The correct answer is 3x3x.

Both numerator terms share 3x, so 6x^2 + 9x = 3x(2x + 3).

5. QuestionMultiple choice

Simplify x2−25x+5\frac{x^2-25}{x+5} for x≠−5x\ne-5.

Please select an answer first.

Correct answer: A

The correct answer is x−5x-5.

  1. Identify the rational-expression structure: Determine the denominators, restrictions, common factors, operation, or equation involved.
  2. Apply the algebraic relationship: Factor the numerator as (x - 5)(x + 5) and cancel x + 5 under the restriction.
  3. Check restrictions and the result: The correct answer is x−5x-5.

Factor the numerator as (x - 5)(x + 5) and cancel x + 5 under the restriction.

6. QuestionMultiple choice

What is 2x3⋅94x\frac{2x}{3}\cdot\frac{9}{4x} for x≠0x\ne0?

Please select an answer first.

Correct answer: B

The correct answer is 32\frac{3}{2}.

  1. Identify the rational-expression structure: Determine the denominators, restrictions, common factors, operation, or equation involved.
  2. Apply the algebraic relationship: Multiply and cancel: (2x)(9)/(3)(4x) = 18x/12x = 3/2.
  3. Check restrictions and the result: The correct answer is 32\frac{3}{2}.

Multiply and cancel: (2x)(9)/(3)(4x) = 18x/12x = 3/2.

7. QuestionMultiple choice

What is xx+1÷2xx+1\frac{x}{x+1}\div\frac{2x}{x+1}?

Please select an answer first.

Correct answer: C

The correct answer is 12\frac{1}{2}.

  1. Identify the rational-expression structure: Determine the denominators, restrictions, common factors, operation, or equation involved.
  2. Apply the algebraic relationship: Multiply by the reciprocal: x/(x+1) · (x+1)/(2x) = 1/2, with original restrictions retained.
  3. Check restrictions and the result: The correct answer is 12\frac{1}{2}.

Multiply by the reciprocal: x/(x+1) · (x+1)/(2x) = 1/2, with original restrictions retained.

8. QuestionMultiple choice

What is the least common denominator of 1x−2\frac{1}{x-2} and 3x+2\frac{3}{x+2}?

Please select an answer first.

Correct answer: D

The correct answer is (x−2)(x+2)(x-2)(x+2).

  1. Identify the rational-expression structure: Determine the denominators, restrictions, common factors, operation, or equation involved.
  2. Apply the algebraic relationship: The least common denominator includes both distinct linear factors.
  3. Check restrictions and the result: The correct answer is (x−2)(x+2)(x-2)(x+2).

The least common denominator includes both distinct linear factors.

9. QuestionMultiple choice

What is 1x+2x\frac{1}{x}+\frac{2}{x}?

Please select an answer first.

Correct answer: A

The correct answer is 3x\frac{3}{x}.

  1. Identify the rational-expression structure: Determine the denominators, restrictions, common factors, operation, or equation involved.
  2. Apply the algebraic relationship: With the same denominator, add numerators: 1/x + 2/x = 3/x.
  3. Check restrictions and the result: The correct answer is 3x\frac{3}{x}.

With the same denominator, add numerators: 1/x + 2/x = 3/x.

10. QuestionMultiple choice

Why must domain restrictions remain after simplifying a rational expression?

Please select an answer first.

Correct answer: B

The correct answer is Canceling a factor does not restore a value that made the original denominator zero..

  1. Identify the rational-expression structure: Determine the denominators, restrictions, common factors, operation, or equation involved.
  2. Apply the algebraic relationship: The simplified formula may be defined at a removed value, but the original expression was undefined there.
  3. Check restrictions and the result: The correct answer is Canceling a factor does not restore a value that made the original denominator zero..

The simplified formula may be defined at a removed value, but the original expression was undefined there.

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