To simplify the expression \(\left(3xy - 2xz + yz\right) + \left(2xy - 4xz - 5yz\right)\), we can combine like terms.
-
Start by writing out the expression: \[ 3xy - 2xz + yz + 2xy - 4xz - 5yz \]
-
Next, group the like terms together:
- \(xy\) terms: \(3xy + 2xy\)
- \(xz\) terms: \(-2xz - 4xz\)
- \(yz\) terms: \(yz - 5yz\)
-
Now, perform the addition for each group:
- For the \(xy\) terms: \[ 3xy + 2xy = 5xy \]
- For the \(xz\) terms: \[ -2xz - 4xz = -6xz \]
- For the \(yz\) terms: \[ yz - 5yz = -4yz \]
-
Combining all these results, we obtain: \[ 5xy - 6xz - 4yz \]
Thus, the expression equivalent to \(\left(3xy - 2xz + yz\right) + \left(2xy - 4xz - 5yz\right)\) is: \[ \boxed{5xy - 6xz - 4yz} \]