## Introductory Algebra for College Students (7th Edition)

$1$
Step by step multiplication of rational expressions: 1. Factor completely what you can 2. Reduce (divide) numerators and denominators by common factors. 3. Multiply the remaining factors in the numerators and multiply the remaining factors in the denominators. $(\displaystyle \frac{P}{Q}\cdot\frac{R}{S}=\frac{PR}{QS})$ --- Factor what we can: $x^{2}+9x+18=...$ ... factor the trinomial $x^{2}+bx+c$ ... by searching for two factors of $c$ whose sum is $b$. ... Here, we find that $6$ and $3$are factors of $18$ whose sum is $9.$ $=(x+3)(x+6)$ The problem becomes $...=\displaystyle \frac{(x+3)(x+6)\cdot 1}{(x+6)\cdot(x+3)}\qquad$... divide out the common factors $=\displaystyle \frac{1}{1}$ = $1$