Question

simplify the complex rational expression.
\\(\frac{\frac{x}{9} - 1}{x - 9}\\)
\\(\bigcirc\\) a. \\(-9\\)
\\(\bigcirc\\) b. \\(x - 9\\)
\\(\bigcirc\\) c. \\(\frac{1}{9}\\)
\\(\bigcirc\\) d. \\(\frac{9}{x - 9}\\)

Explanation:

Step1: Simplify the numerator

First, simplify the numerator $\frac{x}{9} - 1$. We can rewrite $1$ as $\frac{9}{9}$ to have a common denominator:
$\frac{x}{9} - \frac{9}{9} = \frac{x - 9}{9}$

Step2: Rewrite the complex fraction

Now the complex rational expression becomes $\frac{\frac{x - 9}{9}}{x - 9}$. When dividing by a fraction, we multiply by its reciprocal, so this is equivalent to $\frac{x - 9}{9} \times \frac{1}{x - 9}$.

Step3: Cancel common factors

The $(x - 9)$ terms in the numerator and denominator cancel out (assuming $x
eq 9$), leaving us with $\frac{1}{9}$.

Answer:

C. $\frac{1}{9}$