QuestionFind the least common denominator of $\frac{16}{x-9}$ and $\frac{15}{x^{2}-81}$ . What is it?

Studdy Solution

STEP 1

Assumptions1. The rational expressions are $\frac{16}{x-9}$ and $\frac{15}{x^{}-81}$ . . We need to find the least common denominator (LCD) of these expressions.

STEP 2

First, we need to factor the denominators of the rational expressions.
The denominator of the first rational expression is $x-9$ .
The denominator of the second rational expression is $x^{2}-81$ . This is a difference of squares, which can be factored as $(x-9)(x+9)$ .

STEP 3

Now, we write the denominators in factored form.
The denominator of the first rational expression is $x-9$ .
The denominator of the second rational expression is $(x-9)(x+9)$ .

STEP 4

The least common denominator (LCD) is the least common multiple (LCM) of the denominators.The LCM of $x-9$ and $(x-9)(x+9)$ is $(x-9)(x+9)$ .
So, the least common denominator of the rational expressions is $(x-9)(x+9)$ .

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