The first step for solving this problem is to know that in order to divide by a fraction,, we must multiply by the reciprocal of that fraction. This will look like the following:
[tex] \frac{x+2}{ x^{2} -6x-16} [/tex] × 9x
Write -6x as a difference.
[tex] \frac{x+2}{ x^{2} +2x-8x-16} [/tex] × 9x
Factor out x from x² + 2x.
[tex] \frac{x+2}{ x X (x+2)-8x-16} [/tex] × 9x
Factor out -8 from -8(x + 2).
[tex] \frac{x+2}{ x X (x+2)-8(x+2)} [/tex] × 9x
Factor out x + 2 from the denominator (bottom) of the expression.
[tex] \frac{x+2}{(x+2)X(x-8)} [/tex] × 9x
Reduce the fraction with x + 2
[tex] \frac{1}{x-8} [/tex] × 9x
Finally,, calculate the product to find your final answer.
[tex] \frac{9x}{x-8} [/tex]
This means that the correct answer to your question is going to be option B.
Let me know if you have any further questions.
:)
