Answer:
The least common denominator of the two rational expressions is [tex](x+2)^{2}\cdot (x+3)[/tex].
Step-by-step explanation:
Let be the following rational expressions:
[tex]\frac{x^{3}}{x^{2}+4\cdot x + 4}, \frac{-9}{x^{2}+5\cdot x + 6}[/tex]
Then, we factor each denominator:
[tex]\frac{x^{3}}{(x+2)^{2}}, \frac{-9}{(x+3)\cdot (x+2)}[/tex]
Now, we compare each denominator to find all missing binomials so that each expression may have a common denominator:
[tex]\frac{x^{3}}{(x+2)^{2}} \rightarrow (x+3)[/tex]
[tex]\frac{-9}{(x+3)\cdot (x+2)} \rightarrow (x+2)[/tex]
Hence, we conclude that least common denominator of the two rational expressions is [tex](x+2)^{2}\cdot (x+3)[/tex].
