Multiplying and Dividing Rational Expressions

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

To multiply two rational expressions, multiply the numerators together and the denominators together: $$\frac{a}{b} \times \frac{c}{d} = \frac{a \times c}{b \times d}$$ .

The first step is to multiply by the reciprocal of the divisor: $$\frac{a}{b} \text{ divided by } \frac{c}{d} = \frac{a}{b} \times \frac{d}{c}$$ .

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

The formula for dividing rational expressions is: $$\frac{a}{b} \text{ divided by } \frac{c}{d} = \frac{a \times d}{b \times c}$$ .

A common factor is a number or variable that divides evenly into both the numerator and the denominator.

The least common denominator is the smallest expression that is a multiple of the denominators of the rational expressions.

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

The result is $$\frac{x+2}{x+5}$$ after canceling the common factor $$x-3$$ .

Dividing by zero is undefined, so you must ensure that the denominator is not zero.