The mathematical expression from the image is:

[ \left{ \frac{(-2)^3}{[2 - (-2)^2]} \right} - \left{ \frac{[15 - 3]}{2 - 8} \right} ]

Let's break this down step by step.

Left side expression:

$\frac{(-2)^3}{2 - (-2)^2}$

• $(-2)^3 = -8$
• $(-2)^2 = 4$, so $2 - 4 = -2$

Thus, the left side simplifies to: $\frac{-8}{-2} = 4$

Right side expression:

$\frac{15 - 3}{2 - 8}$

• $15 - 3 = 12$
• $2 - 8 = -6$

Thus, the right side simplifies to: $\frac{12}{-6} = -2$

Final step:

Now subtract the two results: $4 - (-2) = 4 + 2 = 6$

So the final result of the entire expression is 6.

Would you like more details or have any questions?

Here are 5 related questions for further practice:

1. Simplify $\frac{(-3)^4}{3 - (-3)^2}$.
2. Evaluate $\frac{7 - 2^2}{5 - (-2)^3}$.
3. Calculate $\frac{4^3}{9 - 2^2}$.
4. Find the result of $5 - \frac{12}{4 - (-2)^2}$.
5. Simplify $\left\{ \frac{(-5)^2}{3 - (-1)^2} \right\} - \left\{ \frac{10}{4 - (-6)} \right\}$.

Tip: Always handle exponents and parentheses first in expressions to avoid errors!