`x+y-(z-x-[y+z-(x+y-{z+x-(y+z+x)})])` is equal to

Options

A. x
B. y
C. z
D. 0

Answer

To solve the expression \( x + y - (z - x - [y + z - (x + y - \{z + x - (y + z + x)\})]) \), we will follow the order of operations: first, we will simplify the innermost brackets (curly braces), then the square brackets, and finally the round brackets.

### Step-by-step Solution:

1. **Start with the innermost expression:**
\[ y + z + x \]
This expression is already simplified.

2. **Next, simplify the curly braces:**
\[ z + x - (y + z + x) \]
Distributing the negative sign:
\[ z + x - y - z - x \]
Here, \( z - z = 0 \) and \( x - x = 0 \), so we are left with:
\[ -y \]

3. **Now substitute back into the expression:**
\[ x + y - (z - x - [y + z - (-y)]) \]
This simplifies to:
\[ x + y - (z - x - [y + z + y]) \]
Which simplifies to:
\[ x + y - (z - x - [y + z + y]) = x + y - (z - x - (2y + z)) \]

4. **Now simplify the square brackets:**
\[ z - x - (2y + z) \]
Distributing the negative sign:
\[ z - x - 2y - z \]
Here, \( z - z = 0 \), so we are left with:
\[ -x - 2y \]

5. **Now substitute back into the expression:**
\[ x + y - (z - x - (-x - 2y)) \]
This simplifies to:
\[ x + y - (z - x + x + 2y) \]
Which simplifies to:
\[ x + y - (z + 2y) \]

6. **Now simplify the round brackets:**
\[ x + y - z - 2y \]
Combining like terms:
\[ x + (y - 2y) - z = x - y - z \]

7. **Final expression:**
The final simplified expression is:
\[ x - y - z \]

### Final Answer:
The expression \( x + y - (z - x - [y + z - (x + y - \{z + x - (y + z + x)\})]) \) simplifies to \( x - y - z \).