Answer: The required simplified form is [tex]\dfrac{9}{x-8}.[/tex]
Step-by-step explanation: We are given to simplify the following:
[tex]E=\dfrac{x+2}{x^2-6x-16}\div\dfrac{1}{9}~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]
To simplify the above expression, we need to factorize the denominator of the first fraction and then try to divide the terms.
We have
[tex]E\\\\\\=\dfrac{x+2}{x^2-6x-16}\div\dfrac{1}{9}\\\\\\=\dfrac{x+2}{x^2-8x+2x-16}\times9\\\\\\=\dfrac{9(x+2)}{x(x-8)+2(x-8)}\\\\\\=\dfrac{9(x+2)}{(x+2)(x-8)}\\\\\\=\dfrac{9}{x-8}.[/tex]
Thus, the required simplified form is [tex]\dfrac{9}{x-8}.[/tex]
