# How do I know that this is the LCD (Lowest Common Denominator) When presented with the following e

How do I know that this is the LCD (Lowest Common Denominator)
When presented with the following expression :
$\frac{1}{\left(x+1\right)\left(x+2\right)}-\frac{2}{x+1}+\frac{3}{x+2}$
I have used an online calculator to show me the LCD, which is :
$\left(x+2\right)\left(x+1\right)$
Although I can work out the LCD for different algebraic expressions, I am unsure of the methodology behind solving this one. I realise it must be basic but it just has not clicked yet.
If anybody could explain how this is done I would be very grateful.
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Alisa Gilmore
LCD - lowest common denominator. Looking at the given denominators, (x+2)(x+1), (x+1) and (x+2) Their lowest common multiple (LCM) is the LCD of the three fractions, in this case (x+2)(x+1)
For an exact approach, we can use Euclidean algorithm to get the Greatest Common Divisor (GCD). The LCM is basically the product of all three numbers divided by the GCD
In this case, by the Euclidean algorithm, the GCD is (x+2)(x+1). The product of the three numbers is (x+2)(x+1)(x+2)(x+1). Dividing this by the GCD we get simply (x+2)(x+1).

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