The least common denominator (LCD) is the smallest number that can be a common denominator for a set of fractions. It's also known as the lowest common denominator.
The denominators of two fractions are given as:
[tex]x^2+6x+9\text{ and }x^2[/tex]Factoring the first expression:
[tex]x^2+6x+9=(x+3)^2[/tex]It's clear there is no common factor between both denominators. Such expressions and numbers are called to be coprime.
For example, 9 and 25 are coprime, but they are not prime numbers individually.
When two numbers or expressions are coprime, the LCD is just their product.
Therefore the Least Common Denominator is:
[tex]x^2(x+3\text{)}^2[/tex]