Solving rational equations worksheet for Algebra 2

Multiply through by the denominators and the fractions disappear, leaving an ordinary equation. Check what you find: a value that makes a denominator zero is extraneous, and some equations have no solution at all.

Also taught in Precalculus, at its own level and with its own examples.

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Pick more than one for a sheet that mixes them.

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Sigma Prep · sigmaprep.io/worksheets Name Solving Rational Equations Date Period Solve each equation. Solve rational equations $a - \frac{54}{a} = 3$ $p + \frac{6}{p} = - 5$ $r + \frac{18}{r} = 9$ $\frac{12}{a} - 8 = \frac{- 84}{a}$ $\frac{- 4}{n + 11} = \frac{- 6}{n + 9}$ $\frac{- 4}{m - 15} = \frac{- 2}{m - 13}$ $\frac{9}{r + 7} = \frac{- 8}{r - 10}$ $x - \frac{32}{x} = - 4$ $\frac{3}{a + 16} = \frac{1}{a + 14}$ $\frac{- 5}{r} + 8 = \frac{75}{r}$ Solve rational equations and check for extraneous roots $\frac{x}{x + 6} = \frac{- 6}{x + 6} + 3$ $\frac{x}{x - 2} + \frac{5}{x} = \frac{- 14}{x (x - 2)}$ $\frac{x}{x - 1} + \frac{2}{x} = \frac{1}{x (x - 1)}$ $\frac{x}{x - 4} - \frac{9}{x} = \frac{16}{x (x - 4)}$ $\frac{x}{x + 4} + \frac{10}{x} = \frac{16}{x (x + 4)}$ $\frac{x}{x + 1} - \frac{1}{x} = \frac{11}{x (x + 1)}$ $\frac{x}{x + 4} - \frac{8}{x} = \frac{- 47}{x (x + 4)}$ $\frac{x}{x + 2} + \frac{11}{x} = \frac{- 8}{x (x + 2)}$ $\frac{x}{x + 3} - \frac{1}{x} = \frac{9}{x (x + 3)}$ $\frac{x}{x + 2} + \frac{3}{x} = \frac{4}{x (x + 2)}$ Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

Solving Rational Equations

Date Period

Solve each equation.

Solve rational equations
$a - \frac{54}{a} = 3$
$p + \frac{6}{p} = - 5$
$r + \frac{18}{r} = 9$
$\frac{12}{a} - 8 = \frac{- 84}{a}$
$\frac{- 4}{n + 11} = \frac{- 6}{n + 9}$
$\frac{- 4}{m - 15} = \frac{- 2}{m - 13}$
$\frac{9}{r + 7} = \frac{- 8}{r - 10}$
$x - \frac{32}{x} = - 4$
$\frac{3}{a + 16} = \frac{1}{a + 14}$
$\frac{- 5}{r} + 8 = \frac{75}{r}$

Solve rational equations and check for extraneous roots
$\frac{x}{x + 6} = \frac{- 6}{x + 6} + 3$
$\frac{x}{x - 2} + \frac{5}{x} = \frac{- 14}{x (x - 2)}$
$\frac{x}{x - 1} + \frac{2}{x} = \frac{1}{x (x - 1)}$
$\frac{x}{x - 4} - \frac{9}{x} = \frac{16}{x (x - 4)}$
$\frac{x}{x + 4} + \frac{10}{x} = \frac{16}{x (x + 4)}$
$\frac{x}{x + 1} - \frac{1}{x} = \frac{11}{x (x + 1)}$
$\frac{x}{x + 4} - \frac{8}{x} = \frac{- 47}{x (x + 4)}$
$\frac{x}{x + 2} + \frac{11}{x} = \frac{- 8}{x (x + 2)}$
$\frac{x}{x + 3} - \frac{1}{x} = \frac{9}{x (x + 3)}$
$\frac{x}{x + 2} + \frac{3}{x} = \frac{4}{x (x + 2)}$



Sigma Prep · sigmaprep.io/worksheets Name Solving Rational EquationsAnswer keyVersion 1 Date Period Solve each equation. Solve rational equations $a - \frac{54}{a} = 3$ ${- 6, 9}$ $p + \frac{6}{p} = - 5$ ${- 3, - 2}$ $r + \frac{18}{r} = 9$ ${3, 6}$ $\frac{12}{a} - 8 = \frac{- 84}{a}$ ${12}$ $\frac{- 4}{n + 11} = \frac{- 6}{n + 9}$ ${- 15}$ $\frac{- 4}{m - 15} = \frac{- 2}{m - 13}$ ${11}$ $\frac{9}{r + 7} = \frac{- 8}{r - 10}$ ${2}$ $x - \frac{32}{x} = - 4$ ${- 8, 4}$ $\frac{3}{a + 16} = \frac{1}{a + 14}$ ${- 13}$ $\frac{- 5}{r} + 8 = \frac{75}{r}$ ${10}$ Solve rational equations and check for extraneous roots $\frac{x}{x + 6} = \frac{- 6}{x + 6} + 3$ No solution $\frac{x}{x - 2} + \frac{5}{x} = \frac{- 14}{x (x - 2)}$ ${- 4, - 1}$ $\frac{x}{x - 1} + \frac{2}{x} = \frac{1}{x (x - 1)}$ ${- 3}$ $\frac{x}{x - 4} - \frac{9}{x} = \frac{16}{x (x - 4)}$ ${5}$ $\frac{x}{x + 4} + \frac{10}{x} = \frac{16}{x (x + 4)}$ ${- 6}$ $\frac{x}{x + 1} - \frac{1}{x} = \frac{11}{x (x + 1)}$ ${- 3, 4}$ $\frac{x}{x + 4} - \frac{8}{x} = \frac{- 47}{x (x + 4)}$ ${3, 5}$ $\frac{x}{x + 2} + \frac{11}{x} = \frac{- 8}{x (x + 2)}$ ${- 6, - 5}$ $\frac{x}{x + 3} - \frac{1}{x} = \frac{9}{x (x + 3)}$ ${4}$ $\frac{x}{x + 2} + \frac{3}{x} = \frac{4}{x (x + 2)}$ ${- 1}$ 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.

Solve rational equations
$a - \frac{54}{a} = 3$ ${- 6, 9}$
$p + \frac{6}{p} = - 5$ ${- 3, - 2}$
$r + \frac{18}{r} = 9$ ${3, 6}$
$\frac{12}{a} - 8 = \frac{- 84}{a}$ ${12}$
$\frac{- 4}{n + 11} = \frac{- 6}{n + 9}$ ${- 15}$
$\frac{- 4}{m - 15} = \frac{- 2}{m - 13}$ ${11}$
$\frac{9}{r + 7} = \frac{- 8}{r - 10}$ ${2}$
$x - \frac{32}{x} = - 4$ ${- 8, 4}$
$\frac{3}{a + 16} = \frac{1}{a + 14}$ ${- 13}$
$\frac{- 5}{r} + 8 = \frac{75}{r}$ ${10}$

Solve rational equations and check for extraneous roots
$\frac{x}{x + 6} = \frac{- 6}{x + 6} + 3$ No solution
$\frac{x}{x - 2} + \frac{5}{x} = \frac{- 14}{x (x - 2)}$ ${- 4, - 1}$
$\frac{x}{x - 1} + \frac{2}{x} = \frac{1}{x (x - 1)}$ ${- 3}$
$\frac{x}{x - 4} - \frac{9}{x} = \frac{16}{x (x - 4)}$ ${5}$
$\frac{x}{x + 4} + \frac{10}{x} = \frac{16}{x (x + 4)}$ ${- 6}$
$\frac{x}{x + 1} - \frac{1}{x} = \frac{11}{x (x + 1)}$ ${- 3, 4}$
$\frac{x}{x + 4} - \frac{8}{x} = \frac{- 47}{x (x + 4)}$ ${3, 5}$
$\frac{x}{x + 2} + \frac{11}{x} = \frac{- 8}{x (x + 2)}$ ${- 6, - 5}$
$\frac{x}{x + 3} - \frac{1}{x} = \frac{9}{x (x + 3)}$ ${4}$
$\frac{x}{x + 2} + \frac{3}{x} = \frac{4}{x (x + 2)}$ ${- 1}$

How to do these

$\frac{3}{x} + 2 = \frac{9}{x}$

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

The answer is ${3}$ .

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.

What you can put on this worksheet

Clear the fractions, then solve: $\frac{- 12}{v} - 4 = \frac{- 16}{v}$ → ${1}$
Quadratic results and extraneous solutions: $\frac{x^{2}}{x + 4} = \frac{2 x + 24}{x + 4}$ → ${6}$
Squared letters, trinomial and cubic denominators, cross terms: $\frac{k - 5}{2 k} = \frac{2}{2 k} + 3$ → ${- \frac{7}{5}}$
A shared factor hidden by a number: Solve:
$\frac{x}{x - 5} = \frac{x + 5}{2 x - 10} + \frac{6}{2 x^{2} - 10 x}$ → $x = - 1, x = 6$

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.

Algebra 2 is usually taken around 10th or 11th 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.

You pick from 4: clear the fractions, then solve, quadratic results and extraneous solutions, squared letters, trinomial and cubic denominators, cross terms and a shared factor hidden by a number. Tick as many as you want and set how many of each, or let it spread them evenly.

Solving rational equations worksheet for Algebra 2

Select your difficulty

Solve rational equations

Solve rational equations and check for extraneous roots

Solve rational equations

Solve rational equations and check for extraneous roots

How to do these

Where students go wrong

What you can put on this worksheet

Questions about these worksheets

Are these solving rational equations worksheets free?+

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What grade are these solving rational equations worksheets for?+

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Is this a free alternative to Kuta Software for solving rational equations?+

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What do students get wrong with solving rational equations?+