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EastWind [94]
2 years ago
14

Find the least common denominator for these

Mathematics
1 answer:
baherus [9]2 years ago
8 0

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).

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