# Multiplying Rational Expressions

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

- Factor numerators and denominators.
- Look for forms that are equivalent in the numerator and denominator.
- Divide out all forms of one.
- 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.

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

**Answers (not in order):**

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