What can be canceled in a rational expression?

Only common factors of the entire numerator and entire denominator — never individual terms. Factor both completely first; then anything shared cancels.

Why do restrictions matter after canceling?

The original expression is undefined wherever its denominator was zero — and canceling can hide that. The restriction survives even after the factor is gone.

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Algebra 2 practice

Simplifying Rational Expressions — Practice

Factor, cancel common factors, and know what you're allowed to cancel — free, no account, with the reasoning on every question.

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What you'll practice

A rational expression is a fraction of polynomials. Simplifying means factoring top and bottom, then canceling common FACTORS — never individual terms. These questions cover factoring both parts, spotting the illegal term-cancel, and the domain restrictions that canceling hides.

Worked example

Simplify $\frac{x^2 - 9}{x^2 + 5x + 6}$ .

Factor the numerator: $x^2 - 9 = (x-3)(x+3)$ (difference of squares).
Factor the denominator: $x^2 + 5x + 6 = (x+2)(x+3)$ .
Cancel the common factor $(x+3)$ : $\frac{(x-3)(x+3)}{(x+2)(x+3)} = \frac{x-3}{x+2}$ .
Note the restrictions from the ORIGINAL denominator: $x \neq -2, -3$ .

Common mistakes

Canceling terms instead of factors: in $\frac{x^2-9}{x^2+5x+6}$ you cannot cancel the $x^2$ 's — only whole factors cancel.
Losing a restriction: after canceling $(x+3)$ , the value $x = -3$ is still excluded — the original expression was undefined there.
Canceling across addition: $\frac{x+3}{3}$ is not $x + 1$ — the 3's aren't factors of the whole numerator.

Try a few

1. Simplify $\frac{x^2 - 4}{x + 2}$ .

$x - 2$ (for $x \neq -2$ )
$x + 2$
$x^2 - 2$
It cannot be simplified

2. Simplify $\frac{x^2 + 3x}{x^2 - 9}$ .

$\frac{x}{x-3}$
$\frac{x}{x+3}$
$\frac{3x}{-9}$
$\frac{1}{x-3}$

3. Simplify $\frac{2x^2 + 6x}{4x}$ .

$\frac{x+3}{2}$
$\frac{2x+6}{4}$
$\frac{x^2+3x}{2}$
$2x + 3$

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FAQ

What can be canceled in a rational expression?: Only common factors of the entire numerator and entire denominator — never individual terms. Factor both completely first; then anything shared cancels.
Why do restrictions matter after canceling?: The original expression is undefined wherever its denominator was zero — and canceling can hide that. The restriction survives even after the factor is gone.
Is Cramzoo free?: Yes — this skill is one of the free ones. Every unit opens with free skills, no account needed. Premium ($6/month or $30/year) unlocks every skill plus the parent progress dashboard.
How is this different from IXL?: No punishing score. A wrong answer gives you a step-by-step explanation, not a number that drops — and every question is reviewed by a human before you see it.

Related Algebra 2 skills

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