Question

Explain how you find the Least Common Denominator of $x^2+5x+4$and $x^2-16$.

Short answer

The LCD is$\left(x+4\right)\left(x-4\right)\left(x+1\right)$.

Step-by-step solution

Step 1. Given information.

Consider the given information.

$x^2+5x+4\mathrm{and}{x}^2-16$

Step 2. Calculation.

Find the factor of the given expression.

$\begin{array}{l}{x}^2+5x+4=x^2+4x+x+4\\ =x\left(x+4\right)+1\left(x+4\right)\\ =\left(x+4\right)+\left(x+1\right)\end{array}$

And,

$\begin{array}{l}{\mathrm{x}}^2-16={\mathrm{x}}^2-4^2\\ =\left(x+4\right)\left(x-4\right)\end{array}$

Write the least common denominator.

$LCD=\left(x+4\right)\left(x-4\right)\left(x+1\right)$