Question

Find the least common denominator for these

Answer 1

Answer:

The least common denominator of the two rational expressions is $(x+2)^{2}\cdot (x+3)$.

Step-by-step explanation:

Let be the following rational expressions:

$\frac{x^{3}}{x^{2}+4\cdot x + 4}, \frac{-9}{x^{2}+5\cdot x + 6}$

Then, we factor each denominator:

$\frac{x^{3}}{(x+2)^{2}}, \frac{-9}{(x+3)\cdot (x+2)}$

Now, we compare each denominator to find all missing binomials so that each expression may have a common denominator:

$\frac{x^{3}}{(x+2)^{2}} \rightarrow (x+3)$

$\frac{-9}{(x+3)\cdot (x+2)} \rightarrow (x+2)$

Hence, we conclude that least common denominator of the two rational expressions is $(x+2)^{2}\cdot (x+3)$.