-{-[-(a+b-c)}]-{+[-(c-a+b)]}+[-{-a+(-b)}]

Let's simplify the given expression step by step:

The expression is:

\[
-{-[-(a+b-c)]}-\{+[-(c-a+b)]\}+\left[ -\{-a+(-b)\}\right]
\]

### Step 1: Simplify each term individually
1. **First term:** \(-{-[-(a+b-c)]}\)

   Start by simplifying the innermost expression:
   \[
   -(a+b-c) = -a - b + c
   \]
   Then simplify further:
   \[
   -[-a - b + c] = a + b - c
   \]
   Finally:
   \[
   -\{a + b - c\} = -a - b + c
   \]

2. **Second term:** \(\{+[-(c-a+b)]\}\)

   Simplify the expression inside the brackets:
   \[
   -(c-a+b) = -c + a - b
   \]
   Therefore:
   \[
   \{+[-c + a - b]\} = -c + a - b
   \]

3. **Third term:** \(\left[ -\{-a+(-b)\}\right]\)

   Start by simplifying inside the braces:
   \[
   -a + (-b) = -a - b
   \]
   Then:
   \[
   -\{-a - b\} = a + b
   \]

### Step 2: Combine the simplified terms

Substitute the simplified terms back into the original expression:

\[
(-a - b + c) - (c - a + b) + (a + b)
\]

### Step 3: Simplify the final expression

Combine like terms:

\[
-a - b + c - c + a - b + a + b
\]

Simplify by combining like terms:

- The \(a\) and \(-a\) terms cancel each other out.
- The \(b\) and \(-b\) terms cancel each other out.
- The \(c\) and \(-c\) terms cancel each other out.

This leaves us with:

\[
0
\]

So, the simplified expression is:

\(\boxed{0}\)

Would you like further details or have any questions?

Here are 8 related questions to consider:
1. How would the process change if there were coefficients in front of the variables?
2. What if one of the operations was a multiplication instead of an addition or subtraction?
3. How can you check your work in simplifying expressions like these?
4. How does the distribution of negative signs affect the simplification?
5. Can this process be applied to more complex expressions with more terms?
6. How does the simplification process differ when using absolute value signs?
7. What happens if one of the variables is equal to zero?
8. How would the simplification change if parentheses were arranged differently?

**Tip:** When simplifying expressions with multiple layers of parentheses or brackets, always start simplifying from the innermost layer outward.

Learn how to simplify a complex mathematical expression involving addition and subtraction step-by-step. This problem covers algebraic concepts, including simplification of expressions and operations with negative numbers. Suitable for students in Grades 7-9.

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