Worksheets · Algebra 1

Adding and subtracting rational expressions worksheet

Same rule as numeric fractions: you cannot add them until the bottoms match. Easy shares a denominator so there is nothing to find; the harder levels make you build the common denominator, which is the actual skill.

Select your difficulty

Pick more than one for a sheet that mixes them.

Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

Adding and Subtracting Rational Expressions

Date Period

Simplify each expression.

  1. 12a−8−12a+6
  2. −2y−2−5y−1
  3. −3m−8+1m+4
  4. 10b+6+3b+12
  5. −4b−2+5b+7
  6. −8n−12−11n+5
  7. 12m+11+9m+2
  8. −11x+9+7x−9
  9. 2y−5−5y−8
  10. −10v−2+11v−11
  11. 7b−2−4b−4
  12. −7a−10+7a−12
  13. −3y+4+1y+11
  14. 10x−2−10x−5
  15. 4v+8−11v+3
  16. −4m+2−12m−1
  17. −3x+4+2x+7
  18. −3p+10+7p−3
  19. −4a+8+6a−5
  20. 7a+2−7a−10

Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

Adding and Subtracting Rational ExpressionsAnswer keyVersion 1

Date Period

Simplify each expression.

  1. 12a−8−12a+6168(a−8)(a+6)
  2. −2y−2−5y−1−7y+12(y−2)(y−1)
  3. −3m−8+1m+4−2m−20(m−8)(m+4)
  4. 10b+6+3b+1213b+138(b+6)(b+12)
  5. −4b−2+5b+7b−38(b−2)(b+7)
  6. −8n−12−11n+5−19n+92(n−12)(n+5)
  7. 12m+11+9m+221m+123(m+11)(m+2)
  8. −11x+9+7x−9−4x+162(x+9)(x−9)
  9. 2y−5−5y−8−3y+9(y−5)(y−8)
  10. −10v−2+11v−11v+88(v−2)(v−11)
  11. 7b−2−4b−43b−20(b−2)(b−4)
  12. −7a−10+7a−1214(a−10)(a−12)
  13. −3y+4+1y+11−2y−29(y+4)(y+11)
  14. 10x−2−10x−5−30(x−2)(x−5)
  15. 4v+8−11v+3−7v−76(v+8)(v+3)
  16. −4m+2−12m−1−16m−20(m+2)(m−1)
  17. −3x+4+2x+7−x−13(x+4)(x+7)
  18. −3p+10+7p−34p+79(p+10)(p−3)
  19. −4a+8+6a−52a+68(a+8)(a−5)
  20. 7a+2−7a−10−84(a+2)(a−10)

Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

How to do these

3x+2+4x−1

  1. The common denominator is (x + 2)(x - 1).
  2. Multiply each top by what its bottom is missing.
  3. 3(x - 1) + 4(x + 2) on top.

The answer is 7x+5(x+2)(x−1).

Where students go wrong

Adding the tops and the bottoms. 3/(x+2) + 4/(x-1) is not 7/(2x+1). The bottoms have to match before anything can be added, and once they do the bottom stays as it is.

Also called adding algebraic fractions, subtracting algebraic fractions or combining rational expressions.

Questions about these worksheets

Yes. Every adding and subtracting rational expressions sheet is free to print and free to download as a PDF. There is no account to make, no email to hand over and no limit on how many you take.

Yes. The answer key prints on a second page, and you can choose whether it shows each question beside its answer or just the answers in a list.

Yes. Print straight from the page, or download the PDF and print that. The sheet is laid out for paper rather than squeezed off a screen, so there is room to work under each question, and the answer key comes out on its own page.

Algebra 1 is usually taken around 8th or 9th grade, though schools vary and plenty of students meet it earlier or later. Pick the difficulty rather than the grade: the easy level suits a first lesson on it, the hard level suits review before a test.

Yes, as many as you like. The questions are built fresh each time rather than picked from a fixed set of files, so pressing Generate gives a new sheet. That is what you want for a second class, a retake, or two students sitting next to each other.

That is the closest comparison, and Kuta Software is good software. It is also paid software you install on a computer. These worksheets run in a browser tab for free, with no account and nothing to install. Like Kuta, the adding and subtracting rational expressions questions are generated when you ask for them rather than pulled from a fixed set of files, so two classes never get the same sheet, and the answer key comes with it.

Yes. There are three levels, and you can tick more than one for a sheet that mixes them, in which case the questions come out easiest first. The harder levels are not just larger numbers: they ask for something the easy ones do not.

Adding the tops and the bottoms. 3/(x+2) + 4/(x-1) is not 7/(2x+1). The bottoms have to match before anything can be added, and once they do the bottom stays as it is.