Complex fractions worksheet for Algebra 2

Algebra 2 complex fractions come in two kinds: a rational expression over a binomial, which simplifies by factoring and cancelling, and sums or differences of small fractions above and below the bar. For the second kind, multiply every term by the least common denominator of all the small fractions, which clears them in one step.

Also taught in Algebra 1, at its own level and with its own examples.

Select your difficulty

Pick more than one for a sheet that mixes them.

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Sigma Prep · sigmaprep.io/worksheets Name Complex Fractions Date Period Simplify each expression. Simplify a complex fraction $\frac{\frac{3 r^{2} + 21 r - 132}{r + 6}}{r + 11}$ $\frac{\frac{1}{x} + 1}{\frac{1}{x^{2}} - 1}$ $\frac{\frac{2 p^{2} - 4 p - 126}{p - 12}}{p - 9}$ $\frac{1 + \frac{6}{x}}{1 - \frac{36}{x^{2}}}$ $\frac{\frac{2 y^{2} - 14 y + 12}{y + 2}}{y - 1}$ $\frac{1 - \frac{1}{x}}{1 - \frac{1}{x^{2}}}$ $\frac{\frac{6 v^{2} - 30 v - 396}{v - 1}}{v + 6}$ $\frac{1 + \frac{3}{x}}{1 - \frac{9}{x^{2}}}$ $\frac{\frac{2 x^{2} + 6 x - 108}{x + 10}}{x - 6}$ $\frac{1 - \frac{2}{x}}{1 - \frac{4}{x^{2}}}$ $\frac{\frac{3 a^{2} - 12 a - 15}{a + 6}}{a - 5}$ $\frac{\frac{2}{x} + 1}{\frac{4}{x^{2}} - 1}$ $\frac{\frac{6 x^{2} - 84 x + 144}{x - 9}}{x - 2}$ $\frac{1 - \frac{5}{x}}{1 - \frac{25}{x^{2}}}$ $\frac{\frac{2 p^{2} + 10 p + 8}{p - 7}}{p + 4}$ $\frac{1 + \frac{4}{x}}{1 - \frac{16}{x^{2}}}$ $\frac{\frac{3 x^{2} + 12 x - 288}{x - 9}}{x - 8}$ $\frac{\frac{5}{x} + 1}{\frac{25}{x^{2}} - 1}$ $\frac{\frac{5 m^{2} + 90 m + 400}{m + 9}}{m + 8}$ $\frac{1 - \frac{6}{x}}{1 - \frac{36}{x^{2}}}$ Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

Complex Fractions

Date Period

Simplify each expression.

Simplify a complex fraction
$\frac{\frac{3 r^{2} + 21 r - 132}{r + 6}}{r + 11}$
$\frac{\frac{1}{x} + 1}{\frac{1}{x^{2}} - 1}$
$\frac{\frac{2 p^{2} - 4 p - 126}{p - 12}}{p - 9}$
$\frac{1 + \frac{6}{x}}{1 - \frac{36}{x^{2}}}$
$\frac{\frac{2 y^{2} - 14 y + 12}{y + 2}}{y - 1}$
$\frac{1 - \frac{1}{x}}{1 - \frac{1}{x^{2}}}$
$\frac{\frac{6 v^{2} - 30 v - 396}{v - 1}}{v + 6}$
$\frac{1 + \frac{3}{x}}{1 - \frac{9}{x^{2}}}$
$\frac{\frac{2 x^{2} + 6 x - 108}{x + 10}}{x - 6}$
$\frac{1 - \frac{2}{x}}{1 - \frac{4}{x^{2}}}$
$\frac{\frac{3 a^{2} - 12 a - 15}{a + 6}}{a - 5}$
$\frac{\frac{2}{x} + 1}{\frac{4}{x^{2}} - 1}$
$\frac{\frac{6 x^{2} - 84 x + 144}{x - 9}}{x - 2}$
$\frac{1 - \frac{5}{x}}{1 - \frac{25}{x^{2}}}$
$\frac{\frac{2 p^{2} + 10 p + 8}{p - 7}}{p + 4}$
$\frac{1 + \frac{4}{x}}{1 - \frac{16}{x^{2}}}$
$\frac{\frac{3 x^{2} + 12 x - 288}{x - 9}}{x - 8}$
$\frac{\frac{5}{x} + 1}{\frac{25}{x^{2}} - 1}$
$\frac{\frac{5 m^{2} + 90 m + 400}{m + 9}}{m + 8}$
$\frac{1 - \frac{6}{x}}{1 - \frac{36}{x^{2}}}$



Sigma Prep · sigmaprep.io/worksheets Name Complex FractionsAnswer keyVersion 2 Date Period Simplify each expression. Simplify a complex fraction $\frac{\frac{3 r^{2} + 21 r - 132}{r + 6}}{r + 11}$ $\frac{3 (r - 4)}{r + 6}$ $\frac{\frac{1}{x} + 1}{\frac{1}{x^{2}} - 1}$ $\frac{x}{1 - x}$ $\frac{\frac{2 p^{2} - 4 p - 126}{p - 12}}{p - 9}$ $\frac{2 (p + 7)}{p - 12}$ $\frac{1 + \frac{6}{x}}{1 - \frac{36}{x^{2}}}$ $\frac{x}{x - 6}$ $\frac{\frac{2 y^{2} - 14 y + 12}{y + 2}}{y - 1}$ $\frac{2 (y - 6)}{y + 2}$ $\frac{1 - \frac{1}{x}}{1 - \frac{1}{x^{2}}}$ $\frac{x}{x + 1}$ $\frac{\frac{6 v^{2} - 30 v - 396}{v - 1}}{v + 6}$ $\frac{6 (v - 11)}{v - 1}$ $\frac{1 + \frac{3}{x}}{1 - \frac{9}{x^{2}}}$ $\frac{x}{x - 3}$ $\frac{\frac{2 x^{2} + 6 x - 108}{x + 10}}{x - 6}$ $\frac{2 (x + 9)}{x + 10}$ $\frac{1 - \frac{2}{x}}{1 - \frac{4}{x^{2}}}$ $\frac{x}{x + 2}$ $\frac{\frac{3 a^{2} - 12 a - 15}{a + 6}}{a - 5}$ $\frac{3 (a + 1)}{a + 6}$ $\frac{\frac{2}{x} + 1}{\frac{4}{x^{2}} - 1}$ $\frac{x}{2 - x}$ $\frac{\frac{6 x^{2} - 84 x + 144}{x - 9}}{x - 2}$ $\frac{6 (x - 12)}{x - 9}$ $\frac{1 - \frac{5}{x}}{1 - \frac{25}{x^{2}}}$ $\frac{x}{x + 5}$ $\frac{\frac{2 p^{2} + 10 p + 8}{p - 7}}{p + 4}$ $\frac{2 (p + 1)}{p - 7}$ $\frac{1 + \frac{4}{x}}{1 - \frac{16}{x^{2}}}$ $\frac{x}{x - 4}$ $\frac{\frac{3 x^{2} + 12 x - 288}{x - 9}}{x - 8}$ $\frac{3 (x + 12)}{x - 9}$ $\frac{\frac{5}{x} + 1}{\frac{25}{x^{2}} - 1}$ $\frac{x}{5 - x}$ $\frac{\frac{5 m^{2} + 90 m + 400}{m + 9}}{m + 8}$ $\frac{5 (m + 10)}{m + 9}$ $\frac{1 - \frac{6}{x}}{1 - \frac{36}{x^{2}}}$ $\frac{x}{x + 6}$ Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

Complex FractionsAnswer keyVersion 2

Date Period

Simplify each expression.

Simplify a complex fraction
$\frac{\frac{3 r^{2} + 21 r - 132}{r + 6}}{r + 11}$ $\frac{3 (r - 4)}{r + 6}$
$\frac{\frac{1}{x} + 1}{\frac{1}{x^{2}} - 1}$ $\frac{x}{1 - x}$
$\frac{\frac{2 p^{2} - 4 p - 126}{p - 12}}{p - 9}$ $\frac{2 (p + 7)}{p - 12}$
$\frac{1 + \frac{6}{x}}{1 - \frac{36}{x^{2}}}$ $\frac{x}{x - 6}$
$\frac{\frac{2 y^{2} - 14 y + 12}{y + 2}}{y - 1}$ $\frac{2 (y - 6)}{y + 2}$
$\frac{1 - \frac{1}{x}}{1 - \frac{1}{x^{2}}}$ $\frac{x}{x + 1}$
$\frac{\frac{6 v^{2} - 30 v - 396}{v - 1}}{v + 6}$ $\frac{6 (v - 11)}{v - 1}$
$\frac{1 + \frac{3}{x}}{1 - \frac{9}{x^{2}}}$ $\frac{x}{x - 3}$
$\frac{\frac{2 x^{2} + 6 x - 108}{x + 10}}{x - 6}$ $\frac{2 (x + 9)}{x + 10}$
$\frac{1 - \frac{2}{x}}{1 - \frac{4}{x^{2}}}$ $\frac{x}{x + 2}$
$\frac{\frac{3 a^{2} - 12 a - 15}{a + 6}}{a - 5}$ $\frac{3 (a + 1)}{a + 6}$
$\frac{\frac{2}{x} + 1}{\frac{4}{x^{2}} - 1}$ $\frac{x}{2 - x}$
$\frac{\frac{6 x^{2} - 84 x + 144}{x - 9}}{x - 2}$ $\frac{6 (x - 12)}{x - 9}$
$\frac{1 - \frac{5}{x}}{1 - \frac{25}{x^{2}}}$ $\frac{x}{x + 5}$
$\frac{\frac{2 p^{2} + 10 p + 8}{p - 7}}{p + 4}$ $\frac{2 (p + 1)}{p - 7}$
$\frac{1 + \frac{4}{x}}{1 - \frac{16}{x^{2}}}$ $\frac{x}{x - 4}$
$\frac{\frac{3 x^{2} + 12 x - 288}{x - 9}}{x - 8}$ $\frac{3 (x + 12)}{x - 9}$
$\frac{\frac{5}{x} + 1}{\frac{25}{x^{2}} - 1}$ $\frac{x}{5 - x}$
$\frac{\frac{5 m^{2} + 90 m + 400}{m + 9}}{m + 8}$ $\frac{5 (m + 10)}{m + 9}$
$\frac{1 - \frac{6}{x}}{1 - \frac{36}{x^{2}}}$ $\frac{x}{x + 6}$

How to do these

$\frac{\frac{1}{x} + \frac{1}{2}}{\frac{1}{x} - \frac{1}{4}}$

The LCD of x, 2 and 4 is 4x.
Top: 4x(1/x + 1/2) = 4 + 2x.
Bottom: 4x(1/x - 1/4) = 4 - x.

The answer is $\frac{2 x + 4}{4 - x}$ .

Where students go wrong

Multiplying only some of the terms by the LCD. Every term above and below the main bar has to be multiplied, or the value of the fraction changes.

Also called fraction over a fraction, stacked fractions or compound fractions.

What you can put on this worksheet

A fraction over a fraction: $\frac{\frac{v + 6}{v + 2}}{v - 4}$ → $\frac{v + 6}{(v + 2) (v - 4)}$
Sums inside the fractions: $\frac{1 - \frac{4}{x}}{1 - \frac{16}{x^{2}}}$ → $\frac{x}{x + 4}$
Numbers only, letters that cancel, binomials inside: $\frac{\frac{k}{16} + \frac{k}{2}}{2 k}$ → $\frac{9}{32}$

Questions about these worksheets

Yes. Every complex fractions 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 complex fractions 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 3: a fraction over a fraction, sums inside the fractions and numbers only, letters that cancel, binomials inside. Tick as many as you want and set how many of each, or let it spread them evenly.

Canceling across the long bar before the division is undone. Nothing cancels between the top fraction and the bottom one until the bottom has been flipped and multiplied.

Complex fractions worksheet for Algebra 2

Select your difficulty

Simplify a complex fraction

Simplify a complex fraction

How to do these

Where students go wrong

What you can put on this worksheet

Questions about these worksheets

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