Simplify and state the excluded values: (n^2 + 3n - 28)/(n^2 - n) × (n)/(n + 4)

((n - 4)(n + 7))/((n - 1)(n + 4)); n ≠ -4, 0, 1

Multiplying and dividing rational expressions worksheet for Algebra 2

Algebra 2 versions put a trinomial or a difference of squares in the first fraction, with binomials elsewhere, and mix in monomials in two letters. Factor the polynomial, flip the divisor, cancel across, and multiply what is left, leaving the answer in factored form.

Also taught in Algebra 1, 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 Multiplying and Dividing Rational Expressions Date Period Simplify each expression. Multiply rational expressions $\frac{r^{2} + 7 r - 44}{r + 6} \cdot \frac{r - 10}{r + 11}$ $\frac{v^{2} + 9 v - 10}{v - 12} \cdot \frac{v + 3}{v + 10}$ $\frac{r^{2} - 2 r - 15}{r + 1} \cdot \frac{r - 10}{r - 5}$ $\frac{m^{2} + 10 m + 9}{m + 2} \cdot \frac{m + 3}{m + 9}$ $\frac{x^{2} + 6 x - 55}{x - 1} \cdot \frac{x - 12}{x - 5}$ $\frac{r^{2} - 12 r + 35}{r + 4} \cdot \frac{r - 2}{r - 7}$ $\frac{y^{2} + 21 y + 108}{y - 3} \cdot \frac{y + 5}{y + 9}$ Divide rational expressions $\frac{n^{2} - 8 n - 33}{n + 2} \div \frac{n - 11}{n + 5}$ $\frac{a^{2} - 100}{a - 12} \div \frac{a + 10}{a - 9}$ $\frac{n^{2} - 25}{n + 6} \div \frac{n - 5}{n + 4}$ $\frac{m^{2} - 2 m - 99}{m - 9} \div \frac{m + 9}{m - 4}$ $\frac{b^{2} - 8 b + 7}{b - 6} \div \frac{b - 7}{b + 3}$ $\frac{n^{2} + 2 n - 8}{n - 8} \div \frac{n + 4}{n - 7}$ $\frac{r^{2} + 18 r + 77}{r + 5} \div \frac{r + 7}{r - 7}$ Multiply and divide monomial fractions $\frac{1}{9} \div \frac{5 x^{3}}{6 x y}$ $\frac{8 x^{2}}{6 x^{3} y^{3}} \cdot \frac{3 x^{3} y}{9 x}$ $\frac{- 3 x y^{3}}{2 x y} \cdot \frac{2 y^{2}}{2 x^{2} y^{2}}$ $\frac{- 4 x y}{9 x^{2} y^{2}} \cdot \frac{- x^{2} y}{6 x y^{2}}$ $\frac{8 y^{2}}{7 x^{2}} \div \frac{- 3 x}{9 x^{3} y^{2}}$ $\frac{8}{2 x^{2} y^{2}} \div \frac{x}{5 x y^{2}}$ Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

Multiplying and Dividing Rational Expressions

Date Period

Simplify each expression.

Multiply rational expressions
$\frac{r^{2} + 7 r - 44}{r + 6} \cdot \frac{r - 10}{r + 11}$
$\frac{v^{2} + 9 v - 10}{v - 12} \cdot \frac{v + 3}{v + 10}$
$\frac{r^{2} - 2 r - 15}{r + 1} \cdot \frac{r - 10}{r - 5}$
$\frac{m^{2} + 10 m + 9}{m + 2} \cdot \frac{m + 3}{m + 9}$
$\frac{x^{2} + 6 x - 55}{x - 1} \cdot \frac{x - 12}{x - 5}$
$\frac{r^{2} - 12 r + 35}{r + 4} \cdot \frac{r - 2}{r - 7}$
$\frac{y^{2} + 21 y + 108}{y - 3} \cdot \frac{y + 5}{y + 9}$

Divide rational expressions
$\frac{n^{2} - 8 n - 33}{n + 2} \div \frac{n - 11}{n + 5}$
$\frac{a^{2} - 100}{a - 12} \div \frac{a + 10}{a - 9}$
$\frac{n^{2} - 25}{n + 6} \div \frac{n - 5}{n + 4}$
$\frac{m^{2} - 2 m - 99}{m - 9} \div \frac{m + 9}{m - 4}$
$\frac{b^{2} - 8 b + 7}{b - 6} \div \frac{b - 7}{b + 3}$
$\frac{n^{2} + 2 n - 8}{n - 8} \div \frac{n + 4}{n - 7}$
$\frac{r^{2} + 18 r + 77}{r + 5} \div \frac{r + 7}{r - 7}$

Multiply and divide monomial fractions
$\frac{1}{9} \div \frac{5 x^{3}}{6 x y}$
$\frac{8 x^{2}}{6 x^{3} y^{3}} \cdot \frac{3 x^{3} y}{9 x}$
$\frac{- 3 x y^{3}}{2 x y} \cdot \frac{2 y^{2}}{2 x^{2} y^{2}}$
$\frac{- 4 x y}{9 x^{2} y^{2}} \cdot \frac{- x^{2} y}{6 x y^{2}}$
$\frac{8 y^{2}}{7 x^{2}} \div \frac{- 3 x}{9 x^{3} y^{2}}$
$\frac{8}{2 x^{2} y^{2}} \div \frac{x}{5 x y^{2}}$



Sigma Prep · sigmaprep.io/worksheets Name Multiplying and Dividing Rational ExpressionsAnswer keyVersion 2 Date Period Simplify each expression. Multiply rational expressions $\frac{r^{2} + 7 r - 44}{r + 6} \cdot \frac{r - 10}{r + 11}$ $\frac{(r - 4) (r - 10)}{r + 6}$ $\frac{v^{2} + 9 v - 10}{v - 12} \cdot \frac{v + 3}{v + 10}$ $\frac{(v - 1) (v + 3)}{v - 12}$ $\frac{r^{2} - 2 r - 15}{r + 1} \cdot \frac{r - 10}{r - 5}$ $\frac{(r + 3) (r - 10)}{r + 1}$ $\frac{m^{2} + 10 m + 9}{m + 2} \cdot \frac{m + 3}{m + 9}$ $\frac{(m + 1) (m + 3)}{m + 2}$ $\frac{x^{2} + 6 x - 55}{x - 1} \cdot \frac{x - 12}{x - 5}$ $\frac{(x + 11) (x - 12)}{x - 1}$ $\frac{r^{2} - 12 r + 35}{r + 4} \cdot \frac{r - 2}{r - 7}$ $\frac{(r - 5) (r - 2)}{r + 4}$ $\frac{y^{2} + 21 y + 108}{y - 3} \cdot \frac{y + 5}{y + 9}$ $\frac{(y + 12) (y + 5)}{y - 3}$ Divide rational expressions $\frac{n^{2} - 8 n - 33}{n + 2} \div \frac{n - 11}{n + 5}$ $\frac{(n + 3) (n + 5)}{n + 2}$ $\frac{a^{2} - 100}{a - 12} \div \frac{a + 10}{a - 9}$ $\frac{(a - 10) (a - 9)}{a - 12}$ $\frac{n^{2} - 25}{n + 6} \div \frac{n - 5}{n + 4}$ $\frac{(n + 5) (n + 4)}{n + 6}$ $\frac{m^{2} - 2 m - 99}{m - 9} \div \frac{m + 9}{m - 4}$ $\frac{(m - 11) (m - 4)}{m - 9}$ $\frac{b^{2} - 8 b + 7}{b - 6} \div \frac{b - 7}{b + 3}$ $\frac{(b - 1) (b + 3)}{b - 6}$ $\frac{n^{2} + 2 n - 8}{n - 8} \div \frac{n + 4}{n - 7}$ $\frac{(n - 2) (n - 7)}{n - 8}$ $\frac{r^{2} + 18 r + 77}{r + 5} \div \frac{r + 7}{r - 7}$ $\frac{(r + 11) (r - 7)}{r + 5}$ Multiply and divide monomial fractions $\frac{1}{9} \div \frac{5 x^{3}}{6 x y}$ $\frac{2 y}{15 x^{2}}$ $\frac{8 x^{2}}{6 x^{3} y^{3}} \cdot \frac{3 x^{3} y}{9 x}$ $\frac{4 x}{9 y^{2}}$ $\frac{- 3 x y^{3}}{2 x y} \cdot \frac{2 y^{2}}{2 x^{2} y^{2}}$ $- \frac{3 y^{2}}{2 x^{2}}$ $\frac{- 4 x y}{9 x^{2} y^{2}} \cdot \frac{- x^{2} y}{6 x y^{2}}$ $\frac{2}{27 y^{2}}$ $\frac{8 y^{2}}{7 x^{2}} \div \frac{- 3 x}{9 x^{3} y^{2}}$ $- \frac{24 y^{4}}{7}$ $\frac{8}{2 x^{2} y^{2}} \div \frac{x}{5 x y^{2}}$ $\frac{20}{x^{2}}$ Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

Multiplying and Dividing Rational ExpressionsAnswer keyVersion 2

Date Period

Simplify each expression.

Multiply rational expressions
$\frac{r^{2} + 7 r - 44}{r + 6} \cdot \frac{r - 10}{r + 11}$ $\frac{(r - 4) (r - 10)}{r + 6}$
$\frac{v^{2} + 9 v - 10}{v - 12} \cdot \frac{v + 3}{v + 10}$ $\frac{(v - 1) (v + 3)}{v - 12}$
$\frac{r^{2} - 2 r - 15}{r + 1} \cdot \frac{r - 10}{r - 5}$ $\frac{(r + 3) (r - 10)}{r + 1}$
$\frac{m^{2} + 10 m + 9}{m + 2} \cdot \frac{m + 3}{m + 9}$ $\frac{(m + 1) (m + 3)}{m + 2}$
$\frac{x^{2} + 6 x - 55}{x - 1} \cdot \frac{x - 12}{x - 5}$ $\frac{(x + 11) (x - 12)}{x - 1}$
$\frac{r^{2} - 12 r + 35}{r + 4} \cdot \frac{r - 2}{r - 7}$ $\frac{(r - 5) (r - 2)}{r + 4}$
$\frac{y^{2} + 21 y + 108}{y - 3} \cdot \frac{y + 5}{y + 9}$ $\frac{(y + 12) (y + 5)}{y - 3}$

Divide rational expressions
$\frac{n^{2} - 8 n - 33}{n + 2} \div \frac{n - 11}{n + 5}$ $\frac{(n + 3) (n + 5)}{n + 2}$
$\frac{a^{2} - 100}{a - 12} \div \frac{a + 10}{a - 9}$ $\frac{(a - 10) (a - 9)}{a - 12}$
$\frac{n^{2} - 25}{n + 6} \div \frac{n - 5}{n + 4}$ $\frac{(n + 5) (n + 4)}{n + 6}$
$\frac{m^{2} - 2 m - 99}{m - 9} \div \frac{m + 9}{m - 4}$ $\frac{(m - 11) (m - 4)}{m - 9}$
$\frac{b^{2} - 8 b + 7}{b - 6} \div \frac{b - 7}{b + 3}$ $\frac{(b - 1) (b + 3)}{b - 6}$
$\frac{n^{2} + 2 n - 8}{n - 8} \div \frac{n + 4}{n - 7}$ $\frac{(n - 2) (n - 7)}{n - 8}$
$\frac{r^{2} + 18 r + 77}{r + 5} \div \frac{r + 7}{r - 7}$ $\frac{(r + 11) (r - 7)}{r + 5}$

Multiply and divide monomial fractions
$\frac{1}{9} \div \frac{5 x^{3}}{6 x y}$ $\frac{2 y}{15 x^{2}}$
$\frac{8 x^{2}}{6 x^{3} y^{3}} \cdot \frac{3 x^{3} y}{9 x}$ $\frac{4 x}{9 y^{2}}$
$\frac{- 3 x y^{3}}{2 x y} \cdot \frac{2 y^{2}}{2 x^{2} y^{2}}$ $- \frac{3 y^{2}}{2 x^{2}}$
$\frac{- 4 x y}{9 x^{2} y^{2}} \cdot \frac{- x^{2} y}{6 x y^{2}}$ $\frac{2}{27 y^{2}}$
$\frac{8 y^{2}}{7 x^{2}} \div \frac{- 3 x}{9 x^{3} y^{2}}$ $- \frac{24 y^{4}}{7}$
$\frac{8}{2 x^{2} y^{2}} \div \frac{x}{5 x y^{2}}$ $\frac{20}{x^{2}}$

How to do these

$\frac{x^{2} - x - 12}{x + 2} \div \frac{x - 4}{x + 5}$

Flip the divisor and factor: (x - 4)(x + 3) over (x + 2), times (x + 5) over (x - 4).
Cancel x - 4.
Multiply what is left.

The answer is $\frac{(x + 3) (x + 5)}{x + 2}$ .

Where students go wrong

Flipping the wrong fraction. Only the fraction after the ÷ turns over: multiply by (x + 5)/(x - 4) and leave the first fraction as written.

Also called multiplying algebraic fractions or dividing algebraic fractions.

What you can put on this worksheet

Multiplying two rational expressions: $\frac{v^{2} + 2 v - 24}{v + 2} \cdot \frac{v + 3}{v - 4}$ → $\frac{(v + 6) (v + 3)}{v + 2}$
Dividing, by flipping the second one: $\frac{v^{2} + 2 v - 24}{v + 2} \div \frac{v - 4}{v + 3}$ → $\frac{(v + 6) (v + 3)}{v + 2}$
Monomials only: $\frac{6 y}{7 x^{2}} \cdot \frac{4 x^{2} y^{3}}{8 y^{2}}$ → $\frac{3 y^{2}}{7}$
With every excluded value, the divisor too: Simplify and state the excluded values:
$\frac{n^{2} + 3 n - 28}{n^{2} - n} \cdot \frac{n}{n + 4}$ → $\frac{(n - 4) (n + 7)}{(n - 1) (n + 4)}$ ; $n \neq - 4, 0, 1$
GCFs to take out, opposite factors, trinomials in both: $\frac{7 k - 42}{k + 4} \cdot \frac{k + 4}{14}$ → $\frac{k - 6}{2}$

Questions about these worksheets

Yes. Every multiplying and dividing 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 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 multiplying and dividing 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.

You pick from 5: multiplying two rational expressions, dividing, by flipping the second one, monomials only, with every excluded value, the divisor too and gcfs to take out, opposite factors, trinomials in both. Tick as many as you want and set how many of each, or let it spread them evenly.

Flipping the wrong fraction, or flipping both. Only the one you are dividing by turns over. The other habit worth breaking is multiplying everything out first, which buries the factors you were about to cancel.

Multiplying and dividing rational expressions worksheet for Algebra 2

Select your difficulty

Multiply rational expressions

Divide rational expressions

Multiply and divide monomial fractions

Multiply rational expressions

Divide rational expressions

Multiply and divide monomial fractions

How to do these

Where students go wrong

What you can put on this worksheet

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