Question

Find the Least Common Denominator of Rational Expressions

In the following exercises, find the LCD.

$\frac{6}{n^2-4},\frac{2n}{n^2-4n+4}.$

Short answer

The answer is means LCD is$(n-2)(n+2).$

Step-by-step solution

Step 1. Given Information.

Given two denominators:

$n^2-4and{n}^2-4n+4.$

Step 2. Finding factors.

LCD is Least Common Denominator

Firstly, we will find factors of the denominators:

$$\begin{gathered} n^2-4=(n-2)(n+2) \\ and \\ {n}^2-4n+4={\left(n-2\right)}^2. \end{gathered}$$

Step 3. Calculating LCD. 

We can clearly see we have 4 factors$(n-2),(n-2),(n-2),(n+2).$

Now we will multiply all the distinct factors we get to find the LCD.

So, the final LCD is:$(n-2)(n+2).$