Add and Subtract Rational Expressions with Unlike Denominators: example 8.38

$\begin{array}{cccc}& & & \hfill \text{Find the LCD for}\frac{8}{x^2-2x-3},\frac{3x}{x^2+4x+3}.\hfill \\ \\ \\ \begin{array}{c}\text{Factor each expression completely, lining}\hfill \\ \text{up common factors.}\hfill \\ \text{Bring down the columns.}\hfill \\ \\ \\ \end{array}\hfill & & & \hfill \frac{\begin{array}{c}{x}^2-2x-3=(x+1)(x-2)\hfill \\ x^2+4x+3=(x+1)(x+3)\hfill \end{array}}{\text{LCD}=(x+1)(x-2)(x+3)}\hfill \\ \\ \\ \text{Multiply the factors.}\hfill & & & \hfill \text{The LCD is}\left(x+1\right)\left(x-3\right)\left(x+3\right).\hfill \end{array}$