Question

Find the LCD for$\frac{x}{x^2+8x+15},\frac{5}{x^2+9x+18}$.

Short answer

The LCD of the required expressions is$\left(x+3\right)\left(x+5\right)\left(x+6\right)$.

Step-by-step solution

Given information 

The given expressions is $\frac{x}{x^2+8x+15},\frac{5}{x^2+9x+18}$

The LCD of the expressions

Factorize the Denominator of the expression

$$\begin{gathered} x^2+8x+15=x^2+3x+5x+15 \\ =x\left(x+3\right)+5\left(x+3\right) \\ =\left(x+5\right)\left(x+3\right) \\ {x}^2+9x+18=x^2+6x+3x+18 \\ =x\left(x+6\right)+3\left(x+6\right) \\ =\left(x+3\right)\left(x+6\right) \end{gathered}$$

Multiply the factors =$\left(x+3\right)\left(x+6\right)\left(x+5\right)$

Therefore, the LCD is$\left(x+3\right)\left(x+6\right)\left(x+5\right).$