Rational expressions are fractions with variables in the numerator, denominator, or both—simplify by factoring, watch for values that make the denominator zero, and use common denominators to add. They show up in the algebra-heavy part of ACT Math, usually as one or two questions per test.
Simplifying by factoring
Factor top and bottom, then cancel common factors—not common terms. Example: (x² - 9)/(x - 3) = (x - 3)(x + 3)/(x - 3) = x + 3, provided x ≠ 3. That restriction matters: the original expression is undefined when x = 3 because the denominator is zero.
Multiplying and dividing
Multiply across and factor before canceling. To divide, flip the second fraction and multiply: (2/x) ÷ (4/x²) = (2/x)(x²/4) = x/2. Keep track of restrictions from every denominator you touch along the way.
Adding and subtracting
You need a common denominator—often the product of the two denominators unless they share a factor. Example: 1/x + 2/(x + 1) = (x + 1 + 2x)/(x(x + 1)) = (3x + 1)/(x(x + 1)). If factoring the denominator is the hard part, review factoring quadratics on the ACT.
Domain restrictions
Any value that makes a denominator zero is excluded from the domain. The ACT may ask "for what value of x is the expression undefined?" Set each denominator factor equal to zero and solve. This ties directly to domain and range.
Where this fits in your prep
Rational expressions sit inside the algebra block—see how much algebra is on the ACT. They overlap with polynomials because factoring is the main tool. Master simplify-add-restrict, and these become routine.
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This article offers general ACT prep guidance. The ACT can change from year to year, including its format, scoring, policies, test dates, and fees, so always confirm the latest details on the official ACT website at act.org before you make decisions. ACT® is a registered trademark of ACT, Inc. thirty-six is not affiliated with, endorsed by, or sponsored by ACT.