Question

Find the least common denominator for these

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

Answer 1

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)`.