Question

1. multiply: \\(dfrac{x^2 + 2x + 1}{x^2 - 1} \cdot dfrac{x^2 + 3x + 2}{x^2 + 4x + 4}\\)

options:
\\(dfrac{x + 1}{x - 1}\\)
\\(dfrac{(x + 1)(x - 1)}{(x + 1)(x + 2)}\\)
\\(dfrac{x + 1}{x + 2}\\)
\\(dfrac{(x + 1)(x + 1)}{(x + 2)(x - 1)}\\)

Explanation:

Step1: Factor all polynomials

$x^2+2x+1=(x+1)^2$, $x^2-1=(x+1)(x-1)$, $x^2+3x+2=(x+1)(x+2)$, $x^2+4x+4=(x+2)^2$

Step2: Substitute into original expression

$\frac{(x+1)^2}{(x+1)(x-1)} \cdot \frac{(x+1)(x+2)}{(x+2)^2}$

Step3: Cancel common factors

Cancel $(x+1)$, $(x+1)$, $(x+2)$: $\frac{x+1}{x+2}$

Answer:

$\frac{x+1}{x+2}$