To solve the problem, we need to proceed step-by-step:
1. Calculate the value of [tex]\( \frac{13}{5} \)[/tex]:
[tex]\[
\frac{13}{5} = 2.6
\][/tex]
2. Calculate the value of [tex]\( -\frac{12}{7} \)[/tex]:
[tex]\[
-\frac{12}{7} \approx -1.7142857142857142
\][/tex]
3. Sum the results of [tex]\( \frac{13}{5} \)[/tex] and [tex]\( -\frac{12}{7} \)[/tex]:
[tex]\[
2.6 + (-1.7142857142857142) \approx 0.8857142857142859
\][/tex]
4. Calculate the value of [tex]\( -\frac{31}{7} \)[/tex]:
[tex]\[
-\frac{31}{7} \approx -4.428571428571429
\][/tex]
5. Calculate the value of [tex]\( -\frac{1}{2} \)[/tex]:
[tex]\[
-\frac{1}{2} = -0.5
\][/tex]
6. Multiply the results of [tex]\( -\frac{31}{7} \)[/tex] and [tex]\( -\frac{1}{2} \)[/tex]:
[tex]\[
(-4.428571428571429) \times (-0.5) \approx 2.2142857142857144
\][/tex]
7. Divide the sum by the product:
[tex]\[
\frac{0.8857142857142859}{2.2142857142857144} \approx 0.4000000000000001
\][/tex]
Thus, the final result of the division is [tex]\( \boxed{0.4000000000000001} \)[/tex].
