Rational expressions

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Sample questions

State the restriction for 1/(x − (___)).

Simplify (x² − ___²)/(x − ___), where x ≠ ___.

Add a/x and b/x when a = ___, b = ___.

Simplify ((x2 − ___)/(x − ___)) · ((x − ___)/(x + ___)), where x ≠ ___ and x ≠ −___.

Simplify ((x2 − ___)/(x − ___)) ÷ ((x − ___)/(x − ___)), where x ≠ ___ and x ≠ ___.

Rational expressions

A rational expression contains fractions involving polynomials. Its domain is restricted by denominators: no denominator may equal zero. Record excluded values before simplifying.

Operations with rational expressions

For multiplication, factor numerators and denominators and cancel common factors. For addition or subtraction, find a common denominator. Only factors may be cancelled, not separate terms in a sum; retain all restrictions from the original expression in the final result.

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Sample questions