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

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

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: $\frac{x^2-10x+16}{x^2-14x+48}$

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

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

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 $\boxed{{\displaystyle \frac{-x-9}{x-6}}}$