To simplify the given expression, we need to combine the fractions. The expression is:

\[
\frac{4 - x^2}{x - 3} + \frac{2x - x^2}{3 - x} + \frac{5 - 4x}{x - 3}
\]

First, notice that \(3 - x = -(x - 3)\). Therefore, we can rewrite the second fraction as:

\[
\frac{2x - x^2}{3 - x} = \frac{2x - x^2}{-(x - 3)} = -\frac{2x - x^2}{x - 3}
\]

Now the expression becomes:

\[
\frac{4 - x^2}{x - 3} - \frac{2x - x^2}{x - 3} + \frac{5 - 4x}{x - 3}
\]

Since all the denominators are now \(x - 3\), we can combine the numerators:

\[
\frac{(4 - x^2) - (2x - x^2) + (5 - 4x)}{x - 3}
\]

Simplify the numerator:

\[
4 - x^2 - 2x + x^2 + 5 - 4x = 4 + 5 - 2x - 4x = 9 - 6x
\]

So the expression simplifies to:

\[
\frac{9 - 6x}{x - 3}
\]

We can factor out a 3 from the numerator:

\[
\frac{3(3 - 2x)}{x - 3}
\]

This is the simplified form of the given expression.