Question

question 27 of 42 which of the following is equal to the rational expression below when x ≠ 2 or 9? \\(\frac{4(x - 2)}{(x - 2)(x - 9)}\\) \\(\bigcirc\\) a. \\(\frac{1}{x - 2}\\) \\(\bigcirc\\) b. \\(\frac{4}{x - 2}\\) \\(\bigcirc\\) c. \\(\frac{4}{x - 9}\\) \\(\bigcirc\\) d. \\(\frac{4}{x - 9}\\) (note: there may be typographical errors in the original options, but the main content is about simplifying the rational expression and choosing the correct option.)

Explanation:

Step1: Identify Common Factors

The given rational expression is $\frac{4(x - 2)}{(x - 2)(x - 9)}$. Since $x
eq2$, we can cancel the common factor $(x - 2)$ from the numerator and the denominator.

Step2: Simplify the Expression

After canceling $(x - 2)$, we get $\frac{4}{x - 9}$.

Answer:

D. $\frac{4}{x - 9}$ (assuming option D is $\frac{4}{x - 9}$ as per the context of simplification)