Sure, let's solve the problem step by step.
1. Convert the mixed numbers to improper fractions:
[tex]\[
3 \frac{1}{3} \text{ can be written as } 3 + \frac{1}{3} = \frac{9}{3} + \frac{1}{3} = \frac{10}{3}
\][/tex]
[tex]\[
2 \frac{1}{2} \text{ can be written as } 2 + \frac{1}{2} = \frac{4}{2} + \frac{1}{2} = \frac{5}{2}
\][/tex]
2. Subtract the improper fractions:
The fractions have different denominators, so we need a common denominator to subtract them. The common denominator for 3 and 2 is 6.
[tex]\[
\frac{10}{3} = \frac{10 \times 2}{3 \times 2} = \frac{20}{6}
\][/tex]
[tex]\[
\frac{5}{2} = \frac{5 \times 3}{2 \times 3} = \frac{15}{6}
\][/tex]
Now subtract them:
[tex]\[
\frac{20}{6} - \frac{15}{6} = \frac{20 - 15}{6} = \frac{5}{6}
\][/tex]
3. Divide the result by [tex]\(\frac{5}{12}\)[/tex]:
Dividing by a fraction is the same as multiplying by its reciprocal.
[tex]\[
\frac{\frac{5}{6}}{\frac{5}{12}} = \frac{5}{6} \times \frac{12}{5}
\][/tex]
Simplify by canceling out the common factors:
[tex]\[
\frac{5 \times 12}{6 \times 5} = \frac{12}{6} = 2
\][/tex]
4. Final result:
The correct answer is [tex]\(2\)[/tex].
So, the simplest form of [tex]\(\frac{3 \frac{1}{3} - 2 \frac{1}{2}}{\frac{5}{12}}\)[/tex] is [tex]\(\boxed{2}\)[/tex].
Thus, the correct option is:
C 2
