The expression you provided is:

$\frac{9}{x} + \frac{-5}{x-3}$

To combine these two terms, we need to find a common denominator. The denominators are $x$ and $x-3$, so the common denominator will be $x(x-3)$.

Now, let's rewrite each fraction with the common denominator:

$\frac{9}{x} = \frac{9(x-3)}{x(x-3)} = \frac{9x - 27}{x(x-3)}$

$\frac{-5}{x-3} = \frac{-5x}{x(x-3)}$

Now, we can combine the two terms:

$\frac{9x - 27}{x(x-3)} + \frac{-5x}{x(x-3)} = \frac{9x - 27 - 5x}{x(x-3)} = \frac{4x - 27}{x(x-3)}$

So the simplified expression is:

$\frac{4x - 27}{x(x-3)}$

Would you like a detailed explanation of how to handle this kind of operation or any specific part of this solution?

Here are 5 related questions to deepen your understanding:

1. How would the expression change if the numerator of the second fraction was positive?
2. What happens to the expression if $x = 3$?
3. Can you find the domain of the simplified expression?
4. What would happen if both numerators were constants?
5. How would you solve for $x$ if this expression were set equal to a number?

Tip: Always watch out for restrictions in the domain when working with rational expressions. In this case, $x \neq 0$ and $x \neq 3$.