#42 **Multiply and Simplify**Given expression to simplify:\[\frac{x - 1}{x^2 + 2x + 1} \cdot \frac{x^2 - 1}{x + 1}\]Options:1. \(\boxed{1}\)2. \(\boxed{\frac{x + 1}{x - 1}}\)3. \(\boxed{\frac{x - 1}{x + 1}}\)4. \(\boxed{\frac{(x - 1)^2}{(x + 1)^2}}\)To solve:1. Factor the denominator and numerator, if possible.2. Simplify the expression by canceling out common terms.**Explanation**First, identify the factorable parts of the numerical expressions. We notice that:- \(x^2 + 2x + 1\) can be written as \((x+1)^2\)- \(x^2 - 1\) can be written as \((x-1)(x+1)\)Rewrite the given expression with these factors:\[\frac{x - 1}{(x + 1)^2} \times \frac{(x - 1)(x + 1)}{x + 1}\]Now, combine the fractions:\[\frac{(x - 1)}{(x + 1)^2} \times \frac{(x - 1)(x + 1)}{x + 1} = \frac{(x - 1) \cdot (x - 1) \cdot (x + 1)}{(x + 1)^2 \cdot (x + 1)}\]Simplify the expression by canceling out common factors. Cancel \((x + 1)\):\[\frac{(x - 1)^2}{(x + 1)^2}\]The simplified form of the given expression is:\[\frac{(x - 1)^2}{(x + 1)^2}\]Hence, the correct answer is:\(\boxed{\frac{(x - 1)^2}{(x + 1)^2}}\)

Name: #42 **Multiply and Simplify**Given expression to simplify:\[\frac{x -
Uploaded: 2024-03-05T11:52:21.000Z
Channel: Bartleby
Description: #42 **Multiply and Simplify**Given expression to simplify:\[\frac{x - 1}{x^2 + 2x + 1} \cdot \frac{x^2 - 1}{x + 1}\]Options:1. \(\boxed{1}\)2. \(\boxed{\frac{x + 1}{x - 1}}\)3. \(\boxed{\frac{x - 1}{x + 1}}\)4. \(\boxed{\frac{(x - 1)^2}{(x + 1)^2}}\)