Worksheets · Precalculus

Precalculus solving rational equations worksheet

Multiply through by the denominators and the fractions disappear, leaving an ordinary equation. Every question here is built from its own solution, so nothing you find will turn out to be extraneous.

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

Solving Rational Equations

Date Period

Solve each equation.

  1. 9a+12=249a
  2. −6p+9=−3p+12
  3. −6p−11=203p
  4. 8v+22=3v+17
  5. −10r−28=−5r−23
  6. −1p+11=−210p
  7. 6a+24=−9a+9
  8. 13y−5=−1y−19
  9. −9k+14=243k
  10. −4y−11=−169y
  11. 12a−1=−3a−16
  12. 8m+21=−2m+11
  13. 7n+11=−202n
  14. 12b+30=−3b+15
  15. 2x+19=−12x+5
  16. −6r+7=4r+17
  17. −5k+14=275k
  18. −1m+11=−221m
  19. −11x+3=−12x+2
  20. −7v−22=11v−4

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

Sigma Prep · sigmaprep.io/worksheets

Name

Solving Rational EquationsAnswer keyVersion 1

Date Period

Solve each equation.

  1. 9a+12=249a{20}
  2. −6p+9=−3p+12{−15}
  3. −6p−11=203p{−19}
  4. 8v+22=3v+17{−14}
  5. −10r−28=−5r−23{18}
  6. −1p+11=−210p{−19}
  7. 6a+24=−9a+9{−18}
  8. 13y−5=−1y−19{18}
  9. −9k+14=243k{18}
  10. −4y−11=−169y{15}
  11. 12a−1=−3a−16{13}
  12. 8m+21=−2m+11{−13}
  13. 7n+11=−202n{−19}
  14. 12b+30=−3b+15{−18}
  15. 2x+19=−12x+5{−17}
  16. −6r+7=4r+17{−13}
  17. −5k+14=275k{20}
  18. −1m+11=−221m{−20}
  19. −11x+3=−12x+2{−14}
  20. −7v−22=11v−4{15}

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

How to do these

3x+2=9x

  1. Multiply everything by x.
  2. 3 + 2x = 9.
  3. 2x = 6.

The answer is x=3.

Where students go wrong

Multiplying only some of the terms. Every term gets multiplied by the denominator, including the ones that are not fractions. The other one is not checking: a value that makes a denominator zero has to be thrown out even if the algebra produced it.

Also called equations with algebraic fractions or solving equations with fractions.

Questions about these worksheets

Yes. Every solving rational equations 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.

Precalculus is usually taken around 11th or 12th 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 solving rational equations 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.

Multiplying only some of the terms. Every term gets multiplied by the denominator, including the ones that are not fractions. The other one is not checking: a value that makes a denominator zero has to be thrown out even if the algebra produced it.