Algebra 2 practice

Complex Fraction Worksheets

Simplify numerical and algebraic complex fractions, with selectable difficulty levels and original-domain restrictions in the answer key.

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Simplify each complex fraction. For expressions with a variable, state all values excluded from the original expression.

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Protect the original domain

Simplify the nested numerator and denominator, then divide by multiplying by the reciprocal.

Learning objective

What this activity builds

Simplify a fraction whose numerator or denominator contains fractions without losing domain restrictions.

Worked example

Simplify (1/x) / (1/(x + 1)).

(x + 1)/x, with x not equal to 0 or -1.

Multiply by the reciprocal. Both original denominators must remain nonzero, so x = -1 stays excluded even though the factor moves to the numerator.

Teaching notes

Make the practice count

Record restrictions before simplifying.
Multiply the complex numerator and denominator by a common denominator.
Cancel factors, not terms in a sum.

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Ten nested-fraction tasks use any nonempty mix of easy numerical, medium one-sided variable, and hard two-sided variable expressions.

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A useful next step

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Practice ten exact quotients with expanded monomials, linear binomials and factorable quadratics, fully reduced answers and all original domain restrictions.

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