To find the difference between the given fractions and express it in simplest form, follow these steps:
1. Write the original problem:
[tex]\[
\frac{u+2}{u-3} - \frac{-2u-7}{u-3}
\][/tex]
2. Since both fractions have the same denominator, subtract the numerators directly:
[tex]\[
\frac{(u+2) - (-2u-7)}{u-3}
\][/tex]
3. Simplify the numerator:
[tex]\[
(u+2) - (-2u-7) = u + 2 + 2u + 7 = u + 2u + 2 + 7 = 3u + 9
\][/tex]
4. Combine the simplified numerator over the common denominator:
[tex]\[
\frac{3u + 9}{u-3}
\][/tex]
5. Factor out the greatest common factor in the numerator (if possible):
Notice that [tex]\(3u + 9\)[/tex] can be factored:
[tex]\[
3(u + 3)
\][/tex]
So, the fraction becomes:
[tex]\[
\frac{3(u + 3)}{u-3}
\][/tex]
This is the simplified form of the given expression. Therefore, the correct answer is:
[tex]\[
\frac{3(u+3)}{u-3}
\][/tex]
