Rational Expressions Practice

A rational expression is a fraction where the numerator and the denominator are both polynomials.

To multiply rational expressions, multiply the numerators together and the denominators together, then simplify if possible.

To divide rational expressions, multiply by the reciprocal of the divisor and then simplify.

Simplifying a rational expression means reducing it to its lowest terms by canceling common factors in the numerator and denominator.

Factoring helps to identify and cancel common factors, making it easier to simplify rational expressions.

The first step is to factor both the numerator and the denominator, then cancel the common factor $$(x+3)$$ .

The result is $$\frac{3(r-2)}{2r(r-5)}$$ , as there are no common factors to cancel.

To simplify complex fractions, find a common denominator for the fractions in the numerator and denominator, then simplify.

The result is $$\frac{1}{c-5}$$ after simplification.

Restrictions are values that make the denominator zero; they must be excluded from the domain of the rational expression.