Let's tackle this problem step-by-step to find the difference and simplify it.
1. Expressing the Fractions:
We start with the two fractions:
[tex]\[
\frac{s + 4}{s - 3} \quad \text{and} \quad \frac{-2s - 5}{s - 3}
\][/tex]
2. Finding the Difference:
We need to subtract the second fraction from the first one:
[tex]\[
\frac{s + 4}{s - 3} - \frac{-2s - 5}{s - 3}
\][/tex]
Since the denominators are the same, we can combine the numerators over the common denominator:
[tex]\[
\frac{(s + 4) - (-2s - 5)}{s - 3}
\][/tex]
Simplify the numerator by distributing the negative sign:
[tex]\[
(s + 4) - (-2s - 5) = s + 4 + 2s + 5 = 3s + 9
\][/tex]
3. Simplified Fraction:
Now we have:
[tex]\[
\frac{3s + 9}{s - 3}
\][/tex]
4. Answer in Simplest Form:
The expression [tex]\(\frac{3s + 9}{s - 3}\)[/tex] is already in its simplest form.
Therefore, the correct simplified difference is:
[tex]\[
\frac{3s + 9}{s - 3}
\][/tex]
So, the correct answer is:
[tex]\[
\boxed{\frac{3s + 9}{s - 3}}
\][/tex]
