Problem 19 - Introductory Algebra for College Students

Question

Multiply as indicated. $$\frac{x^{2}-5 x+6}{x^{2}-2 x-3} \cdot \frac{x^{2}-1}{x^{2}-4}$$

Step-by-Step Solution

Answer

The result of the multiplication of the rational expressions is \(\frac{(x-1)}{(x+2)}\)

Step 1: Factorization

To simplify the multiplication, factorize each polynomial. The factorization result in: \[\frac{(x-2)(x-3)}{(x-3)(x+1)} \cdot \frac{(x+1)(x-1)}{(x-2)(x+2)}\]

Step 2: Multiply the Expressions

Now, multiply the numerators together and denominators together: \[\frac{(x-2)(x-3)(x+1)(x-1)}{(x-3)(x+1)(x-2)(x+2)}\]

Step 3: Simplification

In the resulting expression, cancel out the common factors from the numerator and the denominator: \[\frac{(x-1)}{(x+2)}\]