# How do you find the LCD for x-4 , x+2?

Jan 20, 2016

The LCD of $\left(x - 4\right)$ and $\left(x + 2\right)$ as rational expressions is $1$.

#### Explanation:

LCD is Least Common Divisor.

$\left(x - 4\right)$ and $\left(x + 2\right)$ can be thought of as rational expressions with divisor $1$.

$\left(x - 4\right) = \frac{x - 4}{1}$ and $\left(x + 2\right) = \frac{x + 2}{1}$

Then the only common divisor (scalar or polynomial) they have is $1$.

If you meant to ask what is the LCD of two rational expressions with denominators $\left(x - 4\right)$ and $\left(x + 2\right)$ then the answer is:

$\left(x - 4\right) \left(x + 2\right) = {x}^{2} - 2 x - 8$

The LCD in this case is the LCM (Least Common Multiple) of the two divisors.