Simplify -(x+(-(x+y)-(-x+(y-z)-(-x+y))-y))

$- (x + (- (x + y) - (- x + (y - z) - (- x + y)) - y))$

Remove parentheses.

$- (x - (x + y) - (- x + y - z - (- x + y)) - y)$

Simplify each term.

Apply the distributive property.

$- (x - x - y - (- x + y - z - (- x + y)) - y)$

Simplify each term.

Apply the distributive property.

$- (x - x - y - (- x + y - z - - x - y) - y)$

Multiply $- - x$ .

Multiply $- 1$ by $- 1$ .

$- (x - x - y - (- x + y - z + 1 x - y) - y)$

Multiply $x$ by $1$ .

$- (x - x - y - (- x + y - z + x - y) - y)$

Combine the opposite terms in $- x + y - z + x - y$ .

Add $- x$ and $x$ .

$- (x - x - y - (y - z + 0 - y) - y)$

Add $y - z$ and $0$ .

$- (x - x - y - (y - z - y) - y)$

Subtract $y$ from $y$ .

$- (x - x - y - (- z + 0) - y)$

Add $- z$ and $0$ .

$- (x - x - y - - z - y)$

Multiply $- - z$ .

Multiply $- 1$ by $- 1$ .

$- (x - x - y + 1 z - y)$

Multiply $z$ by $1$ .

$- (x - x - y + z - y)$

Simplify terms.

Subtract $x$ from $x$ .

$- (0 - y + z - y)$

Subtract $y$ from $0$ .

$- (- y + z - y)$

Subtract $y$ from $- y$ .

$- (- 2 y + z)$

Apply the distributive property.

$- (- 2 y) - z$

Multiply $- 2$ by $- 1$ .

$2 y - z$