Problem 20 - Introductory Algebra for College Students

Question

Multiply as indicated. $$\frac{x^{2}+5 x+6}{x^{2}+x-6} \cdot \frac{x^{2}-9}{x^{2}-x-6}$$

Step-by-Step Solution

Answer

\(\frac{{x+3}}{{x-2}}\)

Step 1 Factoring

Factor all the quadratics involved. \[ \frac{{(x+2)(x+3)}}{{(x-2)(x+3)}} \cdot \frac{{(x-3)(x+3)}}{{(x+2)(x-3)}} \]

Step 2 Cancel out common factors

Cross cancel the common factors between the numerator and the denominator. \[ =\frac{{(x+2)}}{{(x-2)}} \cdot \frac{{(x+3)}}{{(x+2)}} \]

Step 3 Multiply the remaining term

Multiply the remaining terms. \[ =\frac{{(x+3)}}{{(x-2)}} \]