Divide Rational Expressions

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

To divide rational expressions, multiply the first expression by the reciprocal of the second expression.

The reciprocal of a fraction is obtained by swapping its numerator and denominator.

(2x^2)/(4x) ÷ (x/3) = (2x^2)/(4x) * (3/x) = (6x)/(4) = (3/2) x.

The first step is to rewrite the division as multiplication by the reciprocal of the second expression.

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

Common factors are terms that appear in both the numerator and denominator that can be canceled out.

The least common denominator is found by identifying the least common multiple of the denominators of the rational expressions.

A polynomial is an algebraic expression that consists of variables, coefficients, and non-negative integer exponents.

Factoring is important because it allows you to identify and cancel common factors in the numerator and denominator.