# Multiplying Rational Expressions

Multiply the rational numbers expressions. Use the same strategies you would use to multiply rational numbers.

1. Factor numerators and denominators.
2. Look for forms that are equivalent in the numerator and denominator.
3. Divide out all forms of one.
4. Multiply the remaining factors in the numerator and denominator (see Factoring from POLQ Module 1 Lesson 3).

Hint: it saves work when all polynomials are factored completely before multiplying.

1. $$\dfrac{x-3}{x+4}\cdot{\dfrac{x+3}{x+7}}$$
2. $$\dfrac{x^2+6x+9}{x^2-9}\cdot{\dfrac{3x-9}{x^2+2x-3}}$$
3. $$\dfrac{2x^2+19x+35}{x^2+x-12}\cdot{\dfrac{2x^2-5x-3}{x^2+4x-21}}$$
4. $$\dfrac{x^2+4x+4}{x-7}\cdot{\dfrac{x-7}{x^2+5x+6}}$$

Answers (not in order):

$$\dfrac{3}{x-1} \hspace{5mm} \dfrac{x+2}{x+3} \hspace{5mm} \dfrac{x^2-9}{x^2+11x+28} \hspace{5mm} \dfrac{4x^2+12x+5}{x^2+x-12}$$