Absolutely, let's solve the given mathematical expression step-by-step:
[tex]\[ (-7-8)\left\{ \left[ \frac{(-4)}{-4+2}-(+9) \right] - \left[ (3+10)-\left(-18+\frac{9}{-3}\right) \right] \right\} \][/tex]
1. Solve innermost parentheses:
[tex]\[
(-4 + 2) = -2
\][/tex]
2. Perform division within the first inner bracket:
[tex]\[
\frac{-4}{-2} = 2
\][/tex]
3. Continue simplifying the first inner bracket:
[tex]\[
2 - (+9) = 2 - 9 = -7
\][/tex]
The expression now becomes:
[tex]\[ (-7-8)\left\{ -7 - \left[ (3+10)-\left(-18+\frac{9}{-3}\right) \right] \right\} \][/tex]
4. Solve the next inner parentheses:
[tex]\[
(3 + 10) = 13
\][/tex]
5. Perform the division in the second bracket:
[tex]\[
\frac{9}{-3} = -3
\][/tex]
6. Continue solving inside the inner brackets:
[tex]\[
-18 + (-3) = -18 - 3 = -21
\][/tex]
The expression is now:
[tex]\[ (-7-8)\left\{ -7 - \left[ 13 - (-21) \right] \right\} \][/tex]
7. Simplify within the brackets:
[tex]\[
13 - (-21) = 13 + 21 = 34
\][/tex]
The expression simplifies to:
[tex]\[ (-7-8)\left\{ -7 - 34 \right\} \][/tex]
8. Combine these terms:
[tex]\[
-7 - 34 = -41
\][/tex]
The original expression now is:
[tex]\[ (-7-8) \times (-41) \][/tex]
9. Finally, solve the multiplication:
[tex]\[
-7 - 8 = -15
\][/tex]
[tex]\[
(-15) \times (-41) = 615
\][/tex]
Thus, the result of the original expression [tex]\[(-7-8)\{[(-4) \div(-4+2)-(+9)]-[(3+10)-(-18+9 \div(-3))]\}\][/tex] is [tex]\(\boxed{615}\)[/tex].
