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Find the least common denominator for these

two rational expressions.
X3/x2+4x+4 -9/x2+5x+6

Find the least common denominator for these two rational expressions. X3/x2+4x+4 -9/x-example-1

1 Answer

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Answer:

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

Explanation:

Let be the following rational expressions:


(x^(3))/(x^(2)+4\cdot x + 4), (-9)/(x^(2)+5\cdot x + 6)

Then, we factor each denominator:


(x^(3))/((x+2)^(2)), (-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:


(x^(3))/((x+2)^(2)) \rightarrow (x+3)


(-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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