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algebra 2 rational expressions quiz - Printable Mathematics Worksheets - Wayground

algebra 2 rational expressions quiz

25 questions

11th - 11th Grade

Mathematics

The Algebra 2 Rational Expressions Quiz is a free printable Grade 11 mathematics worksheet with 25 multiple-choice questions. It gives students repeated practice simplifying rational expressions, then extends that work to multiplying and simplifying rational expressions and finding products. The format requires students to analyze each expression, apply algebraic procedures, and select the equivalent answer from several choices. Use this worksheet to reinforce procedural fluency after instruction, provide independent practice, or check whether students can distinguish a correctly simplified expression from common algebraic errors. Its multiple-choice structure makes it useful for quick formative assessment and review of rational-expression operations. A complete answer key is included with the free printable worksheet, helping teachers check student work efficiently and discuss why particular answer choices are correct or incorrect.

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algebra 2 rational expressions quiz

Total questions: 25

Name
Class
Date
1.

Simplify 7n3n−18+n+33\frac{7n}{3n-18}+\frac{n+3}{3}  

a)

8n+33n−15\frac{8n+3}{3n-15}  

b)

n2+4n−183(n−6)\frac{n^2+4n-18}{3\left(n-6\right)}  

c)

7(n+3)3(3n−18)\frac{7\left(n+3\right)}{3\left(3n-18\right)}  

d)

7n+n+33n−18+3\frac{7n+n+3}{3n-18+3}  

2.

Simplify 8nn−3+3n5n−6\frac{8n}{n-3}+\frac{3n}{5n-6}  

a)

43n2−9(5n−6)(n−3)\frac{43n^2-9}{\left(5n-6\right)\left(n-3\right)}  

b)

11n6n−9\frac{11n}{6n-9}  

c)

43n2−57n(n−3)(5n−6)\frac{43n^2-57n}{\left(n-3\right)\left(5n-6\right)}  

d)

8n+3nn−3+5n−6\frac{8n+3n}{n-3+5n-6}  

3.

Simplify  1n+5×n2+2n−15n−8\frac{1}{n+5}\times\frac{n^2+2n-15}{n-8}  

a)

n−3n−8\frac{n-3}{n-8}  

b)

n−3(n+5)(n−8)\frac{n-3}{\left(n+5\right)\left(n-8\right)}  

c)

n2+2n−15(n+5)(n−8)\frac{n^2+2n-15}{\left(n+5\right)\left(n-8\right)}  

d)

n2+2n−142n−3\frac{n^2+2n-14}{2n-3}  

4.

2a−206a×a−9a−10\frac{2a-20}{6a}\times\frac{a-9}{a-10}  Simplify

a)

2a2−1806a2−60a\frac{2a^2-180}{6a^2-60a}  

b)

2(a−9)6a\frac{2\left(a-9\right)}{6a}  

c)

a−93a\frac{a-9}{3a}  

d)

3a−297a−10\frac{3a-29}{7a-10}  

5.

m2+m−30m2+13m +42÷m−2m+7\frac{m^2+m-30}{m^2+13m\ +42}\div\frac{m-2}{m+7}  Simplify

a)

m−5m−2\frac{m-5}{m-2}  

b)

(m−5)(m−2)(m+7)2\frac{\left(m-5\right)\left(m-2\right)}{\left(m+7\right)^2}  

c)

m2+2m−32m2+14m+49\frac{m^2+2m-32}{m^2+14m+49}  

d)

−52m2\frac{-5}{2m^2}  

6.

28m3−64m2÷18m2\frac{2}{8m^3-64m^2}\div\frac{1}{8m^2}  

a)

2m−64m2\frac{2}{m-64m^2}  

b)

16m28m2(m−8)\frac{16m^2}{8m^2\left(m-8\right)}  

c)

264m4(m−8)\frac{2}{64m^4\left(m-8\right)}  

d)

2m−8\frac{2}{m-8}  

7.

x+1x21x+x+1x\frac{\frac{x+1}{x^2}}{\frac{1}{x}+\frac{x+1}{x}}  Simplify

a)

x+1x2x+2x\frac{\frac{x+1}{x^2}}{\frac{x+2}{x}}  

b)

x+1x(x+2)\frac{x+1}{x\left(x+2\right)}  

c)

2x+2x(x+2)\frac{2x+2}{x\left(x+2\right)}  

d)

1x\frac{1}{x}  

8.

m13+18m\frac{m}{\frac{1}{3}+\frac{18}{m}}  Simplify

a)

3m2m+54\frac{3m^2}{m+54}  

b)

mm+543m\frac{m}{\frac{m+54}{3m}}  

c)

3m+54\frac{3}{m+54}  

d)

3m219\frac{3m^2}{19}  

9.

Simplify x2+x−302x−10\frac{x^2+x-30}{2x-10}  

a)

x+3x+3  

b)

x2−32\frac{x^2-3}{2}  

c)

x+62x−2\frac{x+6}{2x-2}  

d)

x+62\frac{x+6}{2}  

10.

x2+10x+25x2−9⋅x2+3xx+5=\frac{x^2+10x+25}{x^2-9}\cdot\frac{x^2+3x}{x+5}=  

a)

x(x+5)x+3\frac{x\left(x+5\right)}{x+3}  

b)

x(x−5)x−3\frac{x\left(x-5\right)}{x-3}  

c)

x(x+5)x−3\frac{x\left(x+5\right)}{x-3}  

d)

x(x−5)x+3\frac{x\left(x-5\right)}{x+3}  

11.

2m−n8n+6m−3n8n=\frac{2m-n}{8n}+\frac{6m-3n}{8n}=  

a)

m−1m-1  

b)

8m−4n16m2\frac{8m-4n}{16m^2}  

c)

2m−n2n\frac{2m-n}{2n}  

d)

8m+2n8n\frac{8m+2n}{8n}  

12.
a)

A

b)

B

c)

C

d)

D

13.

Simplify:

5x−3x6x2\frac{5}{x}-\frac{3x}{6x^2}  

a)

−33x2x(6x2)\frac{-33x^2}{x\left(6x^2\right)}  

b)

30−3x6x\frac{30-3x}{6x}  

c)

30x−3x6x−6x2\frac{30x-3x}{6x-6x^2}  

d)

27x6x2\frac{27x}{6x^2}  

14.

Simplify:

2x5x−3x+7\frac{2x}{5x}-\frac{3}{x+7}  

a)

2x2−x5x(x+7)\frac{2x^2-x}{5x\left(x+7\right)}  

b)

7x−215x(x+7)\frac{7x-21}{5x\left(x+7\right)}  

c)

2x2+29x5x(x+7)\frac{2x^2+29x}{5x\left(x+7\right)}  

d)

2x2−14x 5x(x+7)\frac{2x^2-14x\ }{5x\left(x+7\right)}  

15.

Simplify: 

52x+8x12x\frac{5}{2x}+\frac{8x}{12x}  

a)

38x12x\frac{38x}{12x}  

b)

8x+3012x\frac{8x+30}{12x}  

c)

25+8x12x\frac{25+8x}{12x}  

d)

76x24x2\frac{76x}{24x^2}  

16.

Multiply and Simplify

a)

4(x+3)/(x+2),

b)

(x+2)/4(x+1)

c)

(x+2)/4(x+3),

d)

4(x+1)/(x+2),

17.

Find the product

a)

A

b)

B

c)

C

d)

D

18.
a)

A

b)

B

c)

C

d)

D

19.
a)

A

b)

B

c)

C

d)

D

20.
a)

A

b)

B

c)

C

d)

D

21.

Simplify:  1y+71y−5\frac{\frac{1}{y}+7}{\frac{1}{y}-5}  

a)

1+7y1−5y\frac{1+7y}{1-5y}  

b)

7+y5−y\frac{7+y}{5-y}  

c)

y+7y−5\frac{y+7}{y-5}  

d)

7(1+y)5(1−y)\frac{7\left(1+y\right)}{5\left(1-y\right)}  

22.

x535\frac{\frac{x}{5}}{\frac{3}{5}}  

a)

5x15\frac{5x}{15}  

b)

3x25\frac{3x}{25}  

c)

x3\frac{x}{3}  

d)

3x\frac{3}{x}  

23.

2xx+13x+1\frac{\frac{2x}{x+1}}{\frac{3}{x+1}}  

a)

2x(x+1)3\frac{2x\left(x+1\right)}{3}  

b)

2x3\frac{2x}{3}  

c)

32x\frac{3}{2x}  

d)

2x(x+1)x+1\frac{2x\left(x+1\right)}{x+1}  

24.

x+3x21−2x\frac{x+\frac{3}{x^2}}{1-\frac{2}{x}}  



a)

x3+3x2−2x\frac{x^3+3}{x^2-2x}  

b)

x(x+3)x−2\frac{x\left(x+3\right)}{x-2}  

c)

x+3x−2\frac{x+3}{x-2}  

d)

x(x3+3)x−2\frac{x\left(x^3+3\right)}{x-2}  

25.

x2−x−2x+6x2−1x+6\frac{\frac{x^2-x-2}{x+6}}{\frac{x^2-1}{x+6}}  



a)

−x−3-x-3  

b)

x2−x−2x2+1\frac{x^2-x-2}{x^2+1}  

c)

x−2(x−1)(x+1)\frac{x-2}{\left(x-1\right)\left(x+1\right)}  

d)

x−2x−1\frac{x-2}{x-1}  

Answer Key

algebra 2 rational expressions quiz

Total questions: 25

1.
b)

n2+4n−183(n−6)\frac{n^2+4n-18}{3\left(n-6\right)}  

2.
c)

43n2−57n(n−3)(5n−6)\frac{43n^2-57n}{\left(n-3\right)\left(5n-6\right)}  

3.
a)

n−3n−8\frac{n-3}{n-8}  

4.
c)

a−93a\frac{a-9}{3a}  

5.
a)

m−5m−2\frac{m-5}{m-2}  

6.
d)

2m−8\frac{2}{m-8}  

7.
b)

x+1x(x+2)\frac{x+1}{x\left(x+2\right)}  

8.
a)

3m2m+54\frac{3m^2}{m+54}  

9.
d)

x+62\frac{x+6}{2}  

10.
c)

x(x+5)x−3\frac{x\left(x+5\right)}{x-3}  

11.
c)

2m−n2n\frac{2m-n}{2n}  

12.
d)

D

13.
d)

27x6x2\frac{27x}{6x^2}  

14.
a)

2x2−x5x(x+7)\frac{2x^2-x}{5x\left(x+7\right)}  

15.
b)

8x+3012x\frac{8x+30}{12x}  

16.
b)

(x+2)/4(x+1)

17.
a)

A

18.
c)

C

19.
b)

B

20.
a)

A

21.
a)

1+7y1−5y\frac{1+7y}{1-5y}  

22.
c)

x3\frac{x}{3}  

23.
b)

2x3\frac{2x}{3}  

24.
a)

x3+3x2−2x\frac{x^3+3}{x^2-2x}  

25.
d)

x−2x−1\frac{x-2}{x-1}  

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FAQs

What does this Algebra 2 rational expressions worksheet cover?

This Grade 11 worksheet contains 25 multiple-choice questions focused mainly on simplifying rational expressions, with additional items on multiplying and simplifying expressions and finding products. Students build fluency by applying algebraic simplification steps and identifying the equivalent expression among several answer choices.

How can I use this worksheet to teach simplifying rational expressions?

Model one rational-expression simplification problem first, emphasizing how students identify and work with common factors before choosing an equivalent form. Then have students complete the multiple-choice items independently or in pairs, asking them to explain why a selected expression is equivalent and why a distractor is not. Use the multiplication and product questions as a transition from simplifying individual expressions to performing rational-expression operations.

What mistakes should I watch for on this rational expressions quiz?

Watch for students cancelling terms across addition or subtraction instead of cancelling common factors, or simplifying only part of a numerator or denominator. In the multiplication and product items, students may combine factors incorrectly or select an answer that reflects an incomplete simplification. Ask students to show their algebraic steps rather than choosing an option without justification.

How do I assign and grade this rational expressions worksheet?

The worksheet is available as a printable PDF and as a digital quiz on Wayground, and it includes a complete answer key for all 25 multiple-choice questions. Printable submissions can be graded by scanning student work with the Wayground for Teachers app. The PDF option can also support classrooms that are reducing screen time.

How can I differentiate this rational expressions worksheet for my students?

Use the worksheet’s Advanced Settings to adjust font spacing and font size so the multiple-choice expressions and answer options are easier to read. You can also apply a dyslexia-friendly font or translate the worksheet into another language when those changes support access to the rational-expression practice. These adjustments change the worksheet file while keeping its 25-question format.

Where can I find more worksheets like this on Wayground?

Wayground offers a comprehensive collection of free printable worksheets and practice problems across all subjects, with downloadable PDFs and answer keys to help students master essential skills and concepts. Browse more worksheets at https://wayground.com/en-us/worksheets.

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