4-3 Simplify, Multiply, and Divide Rational Expressions

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

To simplify a rational expression means to reduce it to its lowest terms by canceling common factors in the numerator and denominator.

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

The domain restriction refers to the values of the variable that make the denominator zero, which are not allowed in the expression.

To find the domain, set the denominator equal to zero and solve for the variable; the solutions are the restrictions.

The result is (x+2)(x+4)/((x+3)(x+5)).

Dividing rational expressions involves multiplying by the reciprocal of the divisor.

To divide, multiply (x+2)/(x+3) by the reciprocal of (x+4)/(x+5), resulting in (x+2)(x+5)/((x+3)(x+4)).

The first step is to factor the numerator and denominator where possible.

Canceling common factors simplifies the expression and helps to find the simplest form.