Answer
$\displaystyle \frac{2x-4}{x-9}$
Work Step by Step
When one denominator is the opposite, or additive inverse of the other,
first multiply either rational expression by $\displaystyle \frac{-1}{-1}$
to obtain a common denominator.
$\displaystyle \frac{4-x}{x-9}-\frac{3x-8}{9-x} \cdot \displaystyle \frac{-1}{-1} = \displaystyle \frac{4-x}{x-9}-\frac{-(3x-8)}{-(9-x)}$
$= \displaystyle \frac{4-x}{x-9}-\frac{-(3x-8)}{9-x} \qquad ... -\displaystyle \frac{-A}{B}=+\frac{A}{B}$
$= \displaystyle \frac{4-x}{x-9}+\frac{(3x-8)}{9-x}$
... To add/subtract rational expressions with the same denominator,
add/subtract numerators and place the sum/difference over the common denominator.
$= \displaystyle \frac{4-x+3x-8}{x-9}$
= $\displaystyle \frac{2x-4}{x-9}$