Find the quotient and simplify the result.
\[
\frac{x+9}{2-x} \div \frac{x^{2}-14 x+48}{x^{2}-10 x+16}
\]
$\frac{x+9}{2-x} \div \frac{x^{2}-14 x+48}{x^{2}-10 x+16}=\square($ Simplify your answer.)

Step 1 ：Given the division of two fractions: \(\frac{x+9}{2-x} \div \frac{x^{2}-14 x+48}{x^{2}-10 x+16}\)

Step 2 ：We know that the division of two fractions is the same as multiplying the first fraction by the reciprocal of the second fraction.

Step 3 ：So, we find the reciprocal of the second fraction: \(\frac{x^{2}-10 x+16}{x^{2}-14 x+48}\)

Step 4 ：Then, we multiply the first fraction by the reciprocal of the second fraction: \(\frac{x+9}{2-x} \times \frac{x^{2}-10 x+16}{x^{2}-14 x+48}\)

Step 5 ：This gives us: \(\frac{(x + 9)*(x^{2} - 10*x + 16)}{(2 - x)*(x^{2} - 14*x + 48)}\)

Step 6 ：We can simplify this result by factoring the polynomials and cancelling out the common factors.

Step 7 ：The simplified result of the division is \(\boxed{\frac{-x - 9}{x - 6}}\)