Follow the steps for graphing a rational function to graph the function \( R(x)=\frac{x+2}{x(x+9)} \). If needed, first write the given function as a single rational expression. Then, factor the numerator and denominator of \( R(x) \). Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. \( R(x)=\square \) (Type your answer in factored form. Do not simplify.) B. \( R(x) \) cannot be factored further.
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To start, we write the given function \( R(x) = \frac{x+2}{x(x+9)} \) as a single rational expression. It is already in this form, so we can move on. Next, let's check if we can factor the numerator and denominator of \( R(x) \): The numerator \( x + 2 \) is a linear expression and cannot be factored further. The denominator \( x(x + 9) \) is already in factored form since it's the product of \( x \) and \( x + 9 \). Combining this information, we can confirm that: A. \( R(x) = \frac{(x + 2)}{x(x + 9)} \) B. Therefore, since the numerator cannot be factored further, the answer is: \( R(x) \) cannot be factored further.
