Simplifying rational expressions worksheet

Factor the top and the bottom, cancel what matches, and stop. Every question here cancels exactly, because the shared factor is chosen before the question is written.

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Pick more than one for a sheet that mixes them.



Sigma Prep · sigmaprep.io/worksheets Name Simplifying Rational Expressions Date Period Simplify each expression. $\frac{a^{2} + 5 a - 84}{a^{2} - 15 a + 56}$ $\frac{3 p^{2} + 12 p - 36}{p^{2} + 3 p - 18}$ $\frac{x^{2} - 13 x + 30}{x^{2} - 16 x + 60}$ $\frac{r^{2} + 4 r - 21}{r^{2} - 9}$ $\frac{p^{2} + 2 p - 120}{p^{2} + 8 p - 48}$ $\frac{b^{2} - 7 b - 18}{b^{2} - 10 b + 9}$ $\frac{k^{2} - 7 k - 60}{k^{2} - 21 k + 108}$ $\frac{y^{2} + 11 y - 12}{y^{2} + 16 y + 48}$ $\frac{v^{2} - 81}{v^{2} + 11 v + 18}$ $\frac{n^{2} - 6 n + 8}{n^{2} + 5 n - 14}$ $\frac{2 x^{2} + 18 x - 44}{x^{2} - 121}$ $\frac{a^{2} + 2 a - 8}{a^{2} - 16}$ $\frac{a^{2} - 4 a - 21}{a^{2} - 3 a - 28}$ $\frac{y^{2} - 1}{y^{2} + 5 y + 4}$ $\frac{2 k^{2} + 12 k - 80}{k^{2} - k - 12}$ $\frac{3 p^{2} + 45 p + 132}{p^{2} + 13 p + 36}$ $\frac{m^{2} + 8 m - 48}{m^{2} - 5 m + 4}$ $\frac{m^{2} + 2 m - 8}{m^{2} + 5 m - 14}$ $\frac{3 a^{2} + 21 a - 90}{a^{2} - 2 a - 3}$ $\frac{a^{2} - 15 a + 44}{a^{2} + a - 20}$ Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

Simplifying Rational Expressions

Date Period

Simplify each expression.

$\frac{a^{2} + 5 a - 84}{a^{2} - 15 a + 56}$
$\frac{3 p^{2} + 12 p - 36}{p^{2} + 3 p - 18}$
$\frac{x^{2} - 13 x + 30}{x^{2} - 16 x + 60}$
$\frac{r^{2} + 4 r - 21}{r^{2} - 9}$
$\frac{p^{2} + 2 p - 120}{p^{2} + 8 p - 48}$
$\frac{b^{2} - 7 b - 18}{b^{2} - 10 b + 9}$
$\frac{k^{2} - 7 k - 60}{k^{2} - 21 k + 108}$
$\frac{y^{2} + 11 y - 12}{y^{2} + 16 y + 48}$
$\frac{v^{2} - 81}{v^{2} + 11 v + 18}$
$\frac{n^{2} - 6 n + 8}{n^{2} + 5 n - 14}$
$\frac{2 x^{2} + 18 x - 44}{x^{2} - 121}$
$\frac{a^{2} + 2 a - 8}{a^{2} - 16}$
$\frac{a^{2} - 4 a - 21}{a^{2} - 3 a - 28}$
$\frac{y^{2} - 1}{y^{2} + 5 y + 4}$
$\frac{2 k^{2} + 12 k - 80}{k^{2} - k - 12}$
$\frac{3 p^{2} + 45 p + 132}{p^{2} + 13 p + 36}$
$\frac{m^{2} + 8 m - 48}{m^{2} - 5 m + 4}$
$\frac{m^{2} + 2 m - 8}{m^{2} + 5 m - 14}$
$\frac{3 a^{2} + 21 a - 90}{a^{2} - 2 a - 3}$
$\frac{a^{2} - 15 a + 44}{a^{2} + a - 20}$



Sigma Prep · sigmaprep.io/worksheets Name Simplifying Rational ExpressionsAnswer keyVersion 1 Date Period Simplify each expression. $\frac{a^{2} + 5 a - 84}{a^{2} - 15 a + 56}$ $\frac{a + 12}{a - 8}$ $\frac{3 p^{2} + 12 p - 36}{p^{2} + 3 p - 18}$ $\frac{3 p - 6}{p - 3}$ $\frac{x^{2} - 13 x + 30}{x^{2} - 16 x + 60}$ $\frac{x - 3}{x - 6}$ $\frac{r^{2} + 4 r - 21}{r^{2} - 9}$ $\frac{r + 7}{r + 3}$ $\frac{p^{2} + 2 p - 120}{p^{2} + 8 p - 48}$ $\frac{p - 10}{p - 4}$ $\frac{b^{2} - 7 b - 18}{b^{2} - 10 b + 9}$ $\frac{b + 2}{b - 1}$ $\frac{k^{2} - 7 k - 60}{k^{2} - 21 k + 108}$ $\frac{k + 5}{k - 9}$ $\frac{y^{2} + 11 y - 12}{y^{2} + 16 y + 48}$ $\frac{y - 1}{y + 4}$ $\frac{v^{2} - 81}{v^{2} + 11 v + 18}$ $\frac{v - 9}{v + 2}$ $\frac{n^{2} - 6 n + 8}{n^{2} + 5 n - 14}$ $\frac{n - 4}{n + 7}$ $\frac{2 x^{2} + 18 x - 44}{x^{2} - 121}$ $\frac{2 x - 4}{x - 11}$ $\frac{a^{2} + 2 a - 8}{a^{2} - 16}$ $\frac{a - 2}{a - 4}$ $\frac{a^{2} - 4 a - 21}{a^{2} - 3 a - 28}$ $\frac{a + 3}{a + 4}$ $\frac{y^{2} - 1}{y^{2} + 5 y + 4}$ $\frac{y - 1}{y + 4}$ $\frac{2 k^{2} + 12 k - 80}{k^{2} - k - 12}$ $\frac{2 k + 20}{k + 3}$ $\frac{3 p^{2} + 45 p + 132}{p^{2} + 13 p + 36}$ $\frac{3 p + 33}{p + 9}$ $\frac{m^{2} + 8 m - 48}{m^{2} - 5 m + 4}$ $\frac{m + 12}{m - 1}$ $\frac{m^{2} + 2 m - 8}{m^{2} + 5 m - 14}$ $\frac{m + 4}{m + 7}$ $\frac{3 a^{2} + 21 a - 90}{a^{2} - 2 a - 3}$ $\frac{3 a + 30}{a + 1}$ $\frac{a^{2} - 15 a + 44}{a^{2} + a - 20}$ $\frac{a - 11}{a + 5}$ Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

Simplifying Rational ExpressionsAnswer keyVersion 1

Date Period

Simplify each expression.

$\frac{a^{2} + 5 a - 84}{a^{2} - 15 a + 56}$ $\frac{a + 12}{a - 8}$
$\frac{3 p^{2} + 12 p - 36}{p^{2} + 3 p - 18}$ $\frac{3 p - 6}{p - 3}$
$\frac{x^{2} - 13 x + 30}{x^{2} - 16 x + 60}$ $\frac{x - 3}{x - 6}$
$\frac{r^{2} + 4 r - 21}{r^{2} - 9}$ $\frac{r + 7}{r + 3}$
$\frac{p^{2} + 2 p - 120}{p^{2} + 8 p - 48}$ $\frac{p - 10}{p - 4}$
$\frac{b^{2} - 7 b - 18}{b^{2} - 10 b + 9}$ $\frac{b + 2}{b - 1}$
$\frac{k^{2} - 7 k - 60}{k^{2} - 21 k + 108}$ $\frac{k + 5}{k - 9}$
$\frac{y^{2} + 11 y - 12}{y^{2} + 16 y + 48}$ $\frac{y - 1}{y + 4}$
$\frac{v^{2} - 81}{v^{2} + 11 v + 18}$ $\frac{v - 9}{v + 2}$
$\frac{n^{2} - 6 n + 8}{n^{2} + 5 n - 14}$ $\frac{n - 4}{n + 7}$
$\frac{2 x^{2} + 18 x - 44}{x^{2} - 121}$ $\frac{2 x - 4}{x - 11}$
$\frac{a^{2} + 2 a - 8}{a^{2} - 16}$ $\frac{a - 2}{a - 4}$
$\frac{a^{2} - 4 a - 21}{a^{2} - 3 a - 28}$ $\frac{a + 3}{a + 4}$
$\frac{y^{2} - 1}{y^{2} + 5 y + 4}$ $\frac{y - 1}{y + 4}$
$\frac{2 k^{2} + 12 k - 80}{k^{2} - k - 12}$ $\frac{2 k + 20}{k + 3}$
$\frac{3 p^{2} + 45 p + 132}{p^{2} + 13 p + 36}$ $\frac{3 p + 33}{p + 9}$
$\frac{m^{2} + 8 m - 48}{m^{2} - 5 m + 4}$ $\frac{m + 12}{m - 1}$
$\frac{m^{2} + 2 m - 8}{m^{2} + 5 m - 14}$ $\frac{m + 4}{m + 7}$
$\frac{3 a^{2} + 21 a - 90}{a^{2} - 2 a - 3}$ $\frac{3 a + 30}{a + 1}$
$\frac{a^{2} - 15 a + 44}{a^{2} + a - 20}$ $\frac{a - 11}{a + 5}$

How to do these

$\frac{x^{2} + 5 x + 6}{x^{2} + 2 x - 3}$

The top factors as (x + 2)(x + 3).
The bottom as (x + 3)(x - 1).
The (x + 3) cancels.

The answer is $\frac{x + 2}{x - 1}$ .

Where students go wrong

Canceling terms rather than factors. In (x + 6)/(x + 2) the x does not cancel, because it is added and not multiplied. Nothing goes until both sides are fully factored.

Also called simplifying algebraic fractions, canceling common factors or reducing rational expressions.

Questions about these worksheets

Yes. Every simplifying 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 simplifying 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.

Canceling terms rather than factors. In (x + 6)/(x + 2) the x does not cancel, because it is added and not multiplied. Nothing goes until both sides are fully factored.

Simplifying rational expressions worksheet

Select your difficulty

Simplifying Rational Expressions

Simplifying Rational ExpressionsAnswer keyVersion 1

How to do these

Where students go wrong

Questions about these worksheets

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