The sum of the sum of x and z and the difference of y and z

The sum of the sum of x and z and the difference of y and z

Take this algebraic expression in 3 parts:

Step 1: The sum of x and z is written as:
x + z

Step 2: The difference of y and z is written as:
y - z

Step 3: the sum of the sum and difference is written as:
x + z + (y - z)
x + z + y - z

Cancelling the z terms, we get:
x + y